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<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for least_common_multiple.cpp:</div>
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Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>tjgurwara99</dd></dl>
<p>A basic implementation of LCM function </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a8ba1fc66e4134ab25b2602b323150563">&#9670;&#160;</a></span>gcd()</h2>
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<td class="memname">unsigned int gcd </td>
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<p>Function for finding greatest common divisor of two numbers. @params two integers x and y whose gcd we want to find. </p><dl class="section return"><dt>Returns</dt><dd>greatest common divisor of x and y. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 16</span> {</div>
<div class="line"><span class="lineno"> 17</span> <span class="keywordflow">if</span> (x == 0) {</div>
<div class="line"><span class="lineno"> 18</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 19</span> }</div>
<div class="line"><span class="lineno"> 20</span> <span class="keywordflow">if</span> (y == 0) {</div>
<div class="line"><span class="lineno"> 21</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><span class="lineno"> 22</span> }</div>
<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">if</span> (x == y) {</div>
<div class="line"><span class="lineno"> 24</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><span class="lineno"> 25</span> }</div>
<div class="line"><span class="lineno"> 26</span> <span class="keywordflow">if</span> (x &gt; y) {</div>
<div class="line"><span class="lineno"> 27</span> <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
<div class="line"><span class="lineno"> 28</span> </div>
<div class="line"><span class="lineno"> 29</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = x / y;</div>
<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
<div class="line"><span class="lineno"> 31</span> }</div>
<div class="line"><span class="lineno"> 32</span> <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
<div class="line"><span class="lineno"> 33</span> </div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
<div class="line"><span class="lineno"> 36</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a></div><div class="ttdeci">unsigned int gcd(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:16</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8d0e241db517813725e721a152e3a25">&#9670;&#160;</a></span>lcm()</h2>
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<td class="memname">unsigned int lcm </td>
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<p>Function for finding the least common multiple of two numbers. @params integer x and y whose lcm we want to find. </p><dl class="section return"><dt>Returns</dt><dd>lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y) </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 43</span> {</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> x / <a class="code hl_function" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
<div class="line"><span class="lineno"> 45</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 78</span> {</div>
<div class="line"><span class="lineno"> 79</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 81</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:50</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Function for testing the <a class="el" href="#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
<div class="line"><span class="lineno"> 51</span> <span class="comment">// First test on lcm(5,10) == 10</span></div>
<div class="line"><span class="lineno"> 52</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 5 and 10 is 10 but lcm function gives a different &quot;</span></div>
<div class="line"><span class="lineno"> 53</span> <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 54</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10) == 10));</div>
<div class="line"><span class="lineno"> 55</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First assertion passes: LCM of 5 and 10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
<div class="line"><span class="lineno"> 56</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 57</span> </div>
<div class="line"><span class="lineno"> 58</span> <span class="comment">// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)</span></div>
<div class="line"><span class="lineno"> 59</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 2 and 3 is 6 but lcm function gives a different &quot;</span></div>
<div class="line"><span class="lineno"> 60</span> <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3) == 6));</div>
<div class="line"><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second assertion passes: LCM of 2 and 3 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
<div class="line"><span class="lineno"> 63</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// Testing an integer overflow.</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="comment">// The algorithm should work as long as the result fits into integer.</span></div>
<div class="line"><span class="lineno"> 67</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 987654321 and 987654321 is 987654321 but lcm function&quot;</span></div>
<div class="line"><span class="lineno"> 68</span> <span class="stringliteral">&quot; gives a different result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321) == 987654321));</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Third assertion passes: LCM of 987654321 and 987654321 is &quot;</span></div>
<div class="line"><span class="lineno"> 71</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321)</div>
<div class="line"><span class="lineno"> 72</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 73</span>}</div>
<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="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="#aa8d0e241db517813725e721a152e3a25">lcm</a></div><div class="ttdeci">unsigned int lcm(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:43</div></div>
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