Question

L.C.M. and H.C.F. of two numbers are 108 and 9 respectively. If one of the two numbers is 54, then the other number is _______

Answer 1

Let, $a$ and $b$ be the two numbers.

Given that, $a=54,$ L.C.M. $=108$ and H.C.F. $=9$

We know that, the product of the L.C.M. and H.C.F. of two numbers is equal to the product of the two numbers.

That is, H.C.F. $\times$ L.C.M. $=a\times b$

$\therefore b=\frac{\text{H.C.F.}\times \text{L.C.M.}}{a}$

$\Rightarrow b=\frac{9\times 108}{54}$

$\therefore b=18$

Hence, the other number is $18$.