Question

The Lowest Common Multiple (LCM) of x and 180 is 360
Find the smallest possible value of x.

Answer 1

Given the LCM of x and 180 is 360, we can use the prime factorization method:

180 =
`2^(2)` ×
`3^(2)` × 5

360 =
`2^(3)` ×
`3^(2)` × 5

Then, we must ensure that the necessary powers are used to make the LCM equal 360. To do this,
`2^(3)`,
`3^(2)`, and 5 must all be prime factors of x.

`2^(3)` ×
`3^(2)` × 5 ⇒ 8 × 9 × 5 ⇒ 360

Because 360 is the only value that meets this criteria, 360 is the smallest possible value of x.