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

Feb 13, 2018

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 $5$: $\text{ } 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , \ldots$

Multiples of $7$: $\text{ } 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70 , 77 , \ldots$

Multiples of $10$: $\text{ } 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , \ldots$

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 $3$: $3 \left(3 \cdot 1\right) , 6 \left(3 \cdot 2\right) , 9 \left(3 \cdot 3\right) , 12 \left(3 \cdot 4\right) , 15 \left(3 \cdot 5\right) , \ldots$

Hope this helps!!

Feb 17, 2018

$70$

#### 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.

$7 \mathmr{and} 10$ do not have any common factors (other than $1$), so their LCM will be their product.

$\therefore L C M = 7 \times 10 = 70$

You can use prime factors to find this as well;

$\text{ } 5 = \textcolor{w h i t e}{w w w} 5$
$\text{ } 7 = \textcolor{w h i t e}{w w w w w} 7$
$\text{ } 10 = \underline{2 \times 5 \textcolor{w h i t e}{w w w}}$

$L C M = 2 \times 5 \times 7 = 70$