Question

What is the LCM of 15, 6, and 9?

Answer 1

`LCM = 90`

Explanation:

Write each number as the product if its prime factors:

`color(white)(xxx)6= 2xx3`
`color(white)(xxx)9 =color(white)(xxx)3xx3`
`color(white)(xxx)15=color(white)(xx)3color(white)(xxx)xx 5`

`LCM = 2xx3xx3xx5 = 90`

OR, using the powers:

`6 = color(blue)(2) xx 3`
`9 = color(blue)(3^2)`
`15 = 3 xx color(blue)(5)`

To find the LCM, use the highest power of each base

`LCM = color(blue)(2xx3^2xx5) = 90`

Or just look at the multiples of `15` (the biggest number) until you find one which is even (because of 6) and divisible by `9` (Sum of the digits must be `9`)

`15,30, 45, 60, 75, color(blue)(90)`