Question

The LCM of two numbers is 45 times their$HCF$ . If one of the numbers is 225 and sum of their LCM and $HCF$ is 1150, find the theother number.

Answer 1

Let the LCM be $x$

The HCF is $45\times x=45x$

Sum of LCM and HCF $x+45x=115046x=1150x=\frac{1150}{46}x=25$

So LCM is $25$ and HCF is $45\times 25=1125$

Let $a,b$ be two numbers

We know that $ab=LCM\times HCF225\times b=25\times 1125b=\frac{28125}{225}b=125$

So the other number is $125$