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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>
<tr class="memitem:a8ba1fc66e4134ab25b2602b323150563"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a> (unsigned int x, unsigned int y)</td></tr>
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<tr class="memitem:aa8d0e241db517813725e721a152e3a25"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a> (unsigned int x, unsigned int y)</td></tr>
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<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</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;&nbsp;</a></span>gcd()</h2>
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<td class="memname">unsigned int gcd </td>
<td>(</td>
<td class="paramtype">unsigned int&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramtype">unsigned int&#160;</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"><a name="l00016"></a><span class="lineno"> 16</span>&#160; {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160; <span class="keywordflow">if</span> (x == 0) {</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160; <span class="keywordflow">return</span> y;</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; }</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; <span class="keywordflow">if</span> (y == 0) {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; }</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordflow">if</span> (x == y) {</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; }</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordflow">if</span> (x &gt; y) {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span> temp = x / y;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; }</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordtype">int</span> temp = y / x;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8d0e241db517813725e721a152e3a25">&#9670;&nbsp;</a></span>lcm()</h2>
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<td class="memname">unsigned int lcm </td>
<td>(</td>
<td class="paramtype">unsigned int&#160;</td>
<td class="paramname"><em>x</em>, </td>
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<td></td>
<td class="paramtype">unsigned int&#160;</td>
<td class="paramname"><em>y</em>&#160;</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"><a name="l00043"></a><span class="lineno"> 43</span>&#160;{ <span class="keywordflow">return</span> x * y / <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</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"><a name="l00067"></a><span class="lineno"> 67</span>&#160; {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&nbsp;</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="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
<div class="fragment"><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="comment">// First test on lcm(5,10) == 10</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; 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"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10) == 10));</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="codeRef" 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" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; &lt;&lt; <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="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; 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"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3) == 6));</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="codeRef" 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" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; &lt;&lt; <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="l00062"></a><span class="lineno"> 62</span>&#160;}</div>
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<div class="ttc" id="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#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>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:48</div></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="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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