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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="title">lcm_sum.cpp File Reference</div> </div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:dd/d47/namespacemath"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
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<tr class="memitem:dd/d47/namespacemath"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft"> </td><td class="mdescRight">for IO operations <br /></td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a> (const uint16_t &num)</td></tr>
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<tr class="separator:a04065193d190d605e1f0d0d93a87e244"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\). </p>
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<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) where \(\mathrm{LCM}(i,n)\) denotes the Least Common Multiple of the integers i and n. For n greater than or equal to 1. The value of the sum is calculated by formula: </p><p class="formulaDsp">
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<div class="textblock"><p >An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\). </p>
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<p >An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) where \(\mathrm{LCM}(i,n)\) denotes the Least Common Multiple of the integers i and n. For n greater than or equal to 1. The value of the sum is calculated by formula: </p><p class="formulaDsp">
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\[ \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d * \mathrm{ETF}(d)) + 1\right) * n\right] \]
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</p>
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<p> where \mathrm{ETF}(i) represents Euler totient function of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/chestamittal">Chesta Mittal</a> </dd></dl>
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<p> where \mathrm{ETF}(i) represents Euler totient function of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/chestamittal" target="_blank">Chesta Mittal</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  {</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <a class="code" href="../../d5/d83/lcm__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> }</div>
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<div class="fragment"><div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> {</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_function" href="../../d5/d83/lcm__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span>}</div>
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<div class="ttc" id="alcm__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d83/lcm__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition:</b> lcm_sum.cpp:65</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<p>Function for testing lcmSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
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<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  {</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  uint64_t n = 2;</div>
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||||
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  uint64_t test_1 = <a class="code" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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||||
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  assert(test_1 == 4);</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 1!"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  </div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  n = 5;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  uint64_t test_2 = <a class="code" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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||||
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  assert(test_2 == 55);</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 2!"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  n = 10;</div>
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||||
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  uint64_t test_3 = <a class="code" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
|
||||
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  assert(test_3 == 320);</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 3!"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  n = 11;</div>
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||||
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  uint64_t test_4 = <a class="code" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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||||
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  assert(test_4 == 616);</div>
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||||
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 4!"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  </div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  n = 15;</div>
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||||
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  uint64_t test_5 = <a class="code" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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||||
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  assert(test_5 == 1110);</div>
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||||
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 5!"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
||||
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> }</div>
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||||
<p >Function for testing lcmSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
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<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> uint64_t n = 2;</div>
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||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> uint64_t test_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> assert(test_1 == 4);</div>
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||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 1!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> n = 5;</div>
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||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> uint64_t test_2 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> assert(test_2 == 55);</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 2!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> n = 10;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> uint64_t test_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> assert(test_3 == 320);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 3!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> n = 11;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> uint64_t test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> assert(test_4 == 616);</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 4!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> n = 15;</div>
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||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> uint64_t test_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> assert(test_5 == 1110);</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 5!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<div class="ttc" id="anamespacemath_html_a04065193d190d605e1f0d0d93a87e244"><div class="ttname"><a href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a></div><div class="ttdeci">uint64_t lcmSum(const uint16_t &num)</div><div class="ttdef"><b>Definition:</b> lcm_sum.cpp:29</div></div>
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@@ -232,7 +231,7 @@ Here is the call graph for this function:</div>
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<ul>
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<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d5/d83/lcm__sum_8cpp.html">lcm_sum.cpp</a></li>
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