Question

What is the Lcm for 5,6,7

Answer 1

210

Explanation:

List the multiples of 5, 6, and 7. (Yes, there are more easier meathods than this.)

The first common multiple is the lowest common multiple (or LCM).

The LCM is 210

Multiples of 5:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100... 210, 215, 220

Multiples of 6:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114... 210, 216, 222

Multiples of 7:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, ... 210, 217, 224

Answer 2

The three numbers have no prime divisors in common:

`5=5,\quad 6=2* 3,\quad 7=7`

So, the least common multiple is the product of the numbers:

`\text{LCM}(5,6,7)=5* 6* 7 = 210`