Question

What is the LCM of 5 6 and 15 ?

Answer 1

The LCM is `30`.

Explanation:

LCM means least common multiple. We can determine the least common multiple by listing the multiples of each number, and then identifying the lowest multiple that they have in common.

`5:` `5,10,15,20,25,color(red)30,35,40...`

`6:` `6,12,18,24,color(red)30,36,42...`

`15:` `15,color(red)30,45,60...`

The lowest multiple in common is `30`.

`"LCM(5,6,15)"=30`.

You can also use prime factorization to find the LCM.

Prime factorize each number.

`5:` `5`

`6:` `2xx3`

`15:` `3xx5`

Multiply each factor the greatest number of times it occurs in each number.

`2:` `"one occurrence"`
`3:` `"one occurrence"`
`5:` `"one occurrence"`

`"LCM(5,6,15)"=2xx3xx5=30`