# How do you find the least common multiple of 6 and 10?

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11
Jim G. Share
Jul 12, 2017

$30$

#### Explanation:

$\text{to find the lowest common multiple (LCM) of 2 numbers}$

• " divide the larger number by the smaller number"

• " if the remainder is zero then the larger number is the LCM"

• " if not repeat with multiples of the larger number"

$\Rightarrow \frac{10}{6} = 1 \textcolor{b l u e}{\text{ remainder 4 }} X$

$\frac{2 \times 10}{6} = \frac{20}{6} = 3 \textcolor{b l u e}{\text{ remainder 2 }} X$

(3xx10)/6=30/6=5color(blue)" remainder 0 " ✔︎

$\Rightarrow \text{ LCM of 6 and 10 } = 30$

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4
Nov 18, 2016

The least common multiple of (6,10) is 30

#### Explanation:

Here's one way to do it :

• Find the prime factors of each number :

$6 = {2}^{1} \times {3}^{1}$
$10 = {2}^{1} \times {5}^{1}$

• Take the larger exponent of each :
in this case : 2, 3 and 5

• Multiply those together to find the LCM :

$2 \times 3 \times 5 = 30$

More examples here to understand :(http://www.coolmath.com/prealgebra/01-gcfs-lcms/04-least-common-multiples-03)

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EET-AP Share
Jul 1, 2017

Multiply the two numbers together to start, then divide that answer by two or five.

#### Explanation:

Rather than trying to find a series of factors for each number in the list it may be more efficient to multiply the numbers together and then factor to find the least common multiple.

In this example, $6 \times 10 = 60$, which is a common multiple CM of the two numbers.

Since we need the least common multiple, try dividing the CM by $2$ or $5$ to find the LCM:

$\textcolor{b l u e}{\frac{60}{2} = 30}$, and $\frac{60}{5} = 12$

Both $6 \mathmr{and} 10$ will multiply into $30$, but $10$ will not multiply into $12$, so $30$ is the LCM or least common multiple.

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