Question

Find two natural numbers whose difference is $66$ and the least common multiple is $360$.

Answer 1

Let the two numbers be $x$ and $x+66$.

Since, the LCM is 360, there must be 5,2 and 3 as the prime factors of the two numbers.

So, one pair is 24 & 90, because $90-24=66$.

Also, $24=2\times 2\times 2\times 3$

$90=2\times 3\times 3\times 5$

$\therefore$ LCM$=2\times 2\times 2\times 3\times 3\times 5=360$.

So, the numbers are $24$ and $90$.