Least Common Multiple
Multiple is a number that can be divided by the given number without leaving a reminder. For example:
20 is a multiple of 5
Or, 5 × 4 = 20
And, 20 ÷ 5 = 4
Least common multiple
The least common multiple of two numbers is the “smallest nonzero common number” which is a multiple of both the numbers.
The different methods to find least common multiple of two or more numbers are:
 Using prime factorization
 Using repeated division
 Using multiples
1. LCM using prime factorization
In this method, a factorization tree for each given number is generated by listing the multiples of that number. The last branch of the tree has the least prime factors for that number.
For example, the factorization trees for 36 and 48 are generated as follows:
Figure: Prime factorization trees for the number 36 and 48
To find the LCM, pair the common multiples as shown. List them along with the remaining multiples.
LCM = 2 × 2 × 3 × 3 × 2 × 2
LCM = 144
2. LCM using repeated division
In this method, the given numbers are divided by the common divisors until there is no possible further division by the common number. The divisors and the remainders are multiplied together to obtain the LCM.
LCM = 2 × 2 × 3 × 4 × 3
LCM = 144
3. LCM using multiples
To find the LCM using multiples, list the multiples of the numbers in the table as shown. The least common multiple is the first common multiple for the given numbers.

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
36 
36 
72 
108 
144 
180 
216 
252 
288 
324 
360 
396 
432 
48 
48 
96 
144 
192 
240 
288 
336 
384 
432 
480 
528 
576 
For 36 and 48, the number 144 is the LCM.
Application
The dimension of using LCM of two numbers starts with basic math operations such as addition and subtraction on fractional numbers. In math problems where we pair two objects against each other, the LCM value is useful in optimizing the quantities of the given objects. Also, in computer science, the LCM of numbers helps design encoded messages using cryptography.
Fun facts

Related math vocabulary
 Multiples and multiplication
 Highest Common Factor (HCF)
 Fractions