Least common multiple of two (or more) numbers is the smallest number that is a multiple (product of the number with any other number) of both the numbers. For example 6 is the smallest multiple of both 2 and 3. Therefore, LCM of 2 and 3 is 6.
Let’s try to find least common multiple of 3 and 4.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
As we can see 12 and 24 both are the multiples of 3 and 4 but 12 is the smallest common multiple. So, least common multiple of 3 and 4 is 12.
Another method of finding LCM is by using the prime factors (numbers which are multiplied) of the numbers of which LCM is to be determined. Follow the following steps:
– Factor each number into its prime factors.
– Count the number of times each prime factor appears for each number
– Take the largest of these counts
– Write down the prime factor as many times as counted in above step
– Multiply all the prime factors to get the LCM of the given numbers
Example:
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
LCM of 12 and 16 = 2 × 2 × 2 × 3 = 48
Factor and Multiple
We often confused between factor and multiple of a number. Let’s take a look below.
Factors are the numbers into which the larger number can be divided. In other words, factors are the numbers which are multiplied to get the larger number. For example, 2 and 3 are the factors of 6 as we get 6 when 2 and 3 are multiplied.
Multiples are the numbers which we get after multiplying the number by another number.
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
So, 6, 9 and 12 are the multiples of 12.