# What is the least common multiple of 3,4, and 6?

Apr 10, 2016

12

#### Explanation:

Mar 28, 2018

The least common multiple of $3 , 4 ,$ and $6$ is $12$

#### Explanation:

The fastest way to find the least common multiple (and also the least common denominator) is usually to start naming the multiples of the largest number.

For each multiple, check to see if the other numbers can also go evenly into that multiple.

Example
Find the least common multiple of $5$ and $6$

1) Use $6$ because it's bigger.
2) Start naming the multiples of $6$

$6 \times 1 = 6$ $\leftarrow$ divisible by $6$ but not by $5$

$6 \times 2 = 12$ $\leftarrow$ divisible by $6$ but not by $5$

$6 \times 3 = 18$ $\leftarrow$ divisible by $6$ but not by $5$

$6 \times 4 = 24$ $\leftarrow$ divisible by $6$ but not by $5$

$6 \times 5 = 30$ $\leftarrow$ $\text{BINGO!}$ $30$ is evenly divisible by both $5$ and $6$

So to find the least common multiple of the numbers in the problem, you do the same procedure.

1) Use $6$ because it's the biggest
2) Start listing the multiples of $6$ until you find one that is also a multiple of $3$ and $4$

$6 \times 1 = 6$$\leftarrow$ Divisible by $3$ and by $6$ but not by $4$

$6 \times 2 = 12$ $\leftarrow$ $\text{BINGO!}$ Divisible by $3 , 4 ,$ and $6$

The LCM (and LCD) of $3 , 4$ and $6$ is 12