Question

What is the lowest common multiple of `5, 7 and 10`?

Answer 1

The answer is `70`.

Explanation:

To find the LCM (Lowest common multiple) of a set of numbers, you first find the multiples of each number and then identify the smallest common one among the set.

In this case, using `5`, `7`, and `10`. The smallest common multiple of each would be `70`. If we find the multiples of each of the numbers, we can see that no other number before `70` is common to all of them.

Multiples of `5`: `" "5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, ...`

Multiples of `7`: `" "7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ...`

Multiples of `10`: `" "10, 20, 30, 40, 50, 60, 70, 80, ...`

If you realize, the only common multiple up to this point is `70`. There may be other common multiples but you are looking for the smallest (or lowest) one.

Note: The way you find multiples is to multiply the number you are trying to find numbers for by each number in succession.

For example, multiples of `3`: `3(3*1), 6(3*2), 9(3*3), 12(3*4), 15(3*5), ...`

Hope this helps!!

Answer 2

`70`

Explanation:

You do not need to consider `5` at all the calculation, because it is a factor of `10`. So any number divisible by `10` will automatically be divisible by `5` as well.

`7 and 10` do not have any common factors (other than `1`), so their LCM will be their product.

`:. LCM = 7 xx10 = 70`

You can use prime factors to find this as well;

`" "5 = color(white)(www) 5`
`" "7 =color(white)(wwwww) 7`
`" "10 = ul(2 xx 5color(white)(www))`

`LCM = 2 xx 5 xx 7 = 70`