Question

The L.C.M. of two numbers is 24 times their H.C.F. The sum of their H.C.F. and L.C.M. is 375. If one number is 45, then what is the other number?

Answer 1

Given that the $LCM$ of two numbers is $24$ times their $HCF$

And that their sum is $375$.

$\therefore LCM+HCF=375$ and $LCM=24\times HCF$

$\Rightarrow 24HCF+HCF=375$

$\Rightarrow 25HCF=375$

$\Rightarrow HCF=\frac{375}{25}$

$=15$

$\therefore LCM=375-15$

$=360$

We know that, the product of the $LCM$ and $HCF$ of two numbers is equal to the product of the numbers.

Also, given that one of the two numbers is $45$.

$\therefore$ Second number = $\frac{LCM\times HCF}{\text{Given number}}$

$=\frac{360\times 15}{45}$

$=120$

Hence, the other number is $120$.