# Finding The Least Common Multiple Is As Easy As One, Two…

The least common multiple of two or more **non-zero** whole numbers is actually the smallest whole number that is **divisible by each** of the numbers.

There are two widely used methods.

## Method 1

**Simply list the multiples** of each number (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.

**Example:**

Find the least common multiple for 5, 6, and 15.

- First we list the multiples of each number.

Multiples of 5 are 10, 15, 20, 25,30, 35, 40,…

Multiples of 6 are 12, 18, 24,30, 36, 42, 48,…

Multiples of 15 are30, 45, 60, 75, 90,….- Now, when you look at the list of multiples, you can see that 30 is the
smallest numberthat appears in each list.- Therefore, the least common multiple of…

… 5, 6 and 15 is30.

### Method 2

To use this method** factor each of the numbers** into primes. Then for each **different** prime number in all of the factorizations, do the following…

**Count**the number of times each prime number appears in each of the factorizations.- For each prime number, take the largest of these counts.
- Write down that prime number as many times as you counted for it in step 2.
- The least common multiple is the
**product**of all the prime numbers written down.

**Example:**

Find the least common multiple of 5, 6 and 15.

**Factor into primes**

Prime factorization of **5** is **5**

Prime factorization of **6** is **2 x 3**

Prime factorization of **15** is **3 x 5**

**Notice** that the different primes are **2**, **3** and **5**.

- Now, we do
**Step #1**–**Count the number of times each prime number appears in each of the factorizations…**

The count of primes in 5 is one**5**

The count of primes in 6 is one**2**and one**3**

The count of primes in 15 is one**3**and one**5** **Step #2 – For each prime number, take the largest of these counts.**So we have…

The largest count of**2s**is**one**

The largest count of**3s**is**one**

The largest count of**5s**is**one****Step #3**– Since we now know the count of each prime number, you simply –**write down that prime number as many times as you counted for it in step 2**.Here they are…

**2, 3, 5****Step #4**– The least common multiple is the**product**of all the prime numbers written down.// Therefore, the least common multiple of 5, 6 and 15 is 30.

2 x 3 x 5 = 30

**So there you have it.**

A quick and easy method for finding least common multiples.