# How do you find the least common multiple of 10, 2, and 15?

Jan 21, 2017

30

#### Explanation:

Observe that 10 is less than 15 so the multiple has to be bigger than 10. Any whole number multiple of 10 will have 0 as its last digit.

2 will be a factor of the LCM so it can not be an odd number.

The multiple of 15 can only have 5 or 0 as its last digit.
So in keeping with the above comments we pick the first multiple of 15 that has a 0 as its last digit (which as it happens, is an even number)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$2 \times 15 = 30$
$3 \times 10 = 30$

So the LCM is 30