Question

The LCM of two numbers is 36.if both the numbers lie between 10 and 20, find the numbers.

Answer 1

LCM is 36 = $2^{2} * 3^{2}$, the conclusion is that the numbers can be of form $2^{p} * 3^{q}$ such that $0 \leq p \leq 2$ and $0 \leq q \leq 2$.

Now there are two combinations for p and q such that numbers is between 10 and 20 -
(1) ; (p, q) = (1, 2) -> number = 18
(2) : (p, q) = (2, 1) -> number = 12

This is the way, you solve it.

Answer = (12, 18) or (18, 12)

Answer 2

$LCM(m;\ n)=36\\\\The\ divisors\ of\ 36:\\1;\ 2;\ 3;\ 4;\ 6;\ 9;\ \fbox{12};\ \fbox{18};\ 36\\\\Answer:12\ and\ 18.$