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<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">M</font> = <font color="Maroon">m</font> <a href="nat_1.html#K8">lcm</a> <font color="Maroon">n</font>;<br/>
<a NAME="E1:72"/>
( <font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="nat_1.html#K8">lcm</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="nat_1.html#K8">lcm</a> <font color="Maroon">n</font> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a> <font color="Olive">k</font> &amp; <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Olive">k</font> holds <br/><font color="Maroon">m</font> <a href="nat_1.html#K8">lcm</a> <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Olive">k</font> ) )
 
<b>by </b><i><a class="ref" href="nat_1.html#D4">NAT_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E2:72"/>
<font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K8">lcm</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i/>;<br/>


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