Least Common Multiple of 18 and 21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 18 and 21 the smallest integer that is 126 that is divisible by both numbers.

Least Common Multiple (LCM) of 18 and 21 is 126.

LCM(18,21) = 126

LCM of 18 and 21

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 18 and 21

LCM of 18 and 21 is 126

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 21. First we will calculate the prime factors of 18 and 21.

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

Prime Factorization of 21


3 21
7 7
1

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 18 and 21.

LCM(18,21) = 21×32×71
LCM(18,21) = 126

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Least Common Multiple of 18 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18 and 21, than apply into the LCM equation.

GCF(18,21) = 3
LCM(18,21) = ( 18 × 21) / 3
LCM(18,21) = 378 / 3
LCM(18,21) = 126

Properties of LCM 18 and 21

(i) The LCM of 21 and 18 is associative

LCM of 18 and 21 = LCM of 21 and 18

Related Least Common Multiples of 18

Related Least Common Multiples of 21

Frequently Asked Questions on LCM of 18 and 21

1. What is the LCM of 18 and 21?

Answer: LCM of 18 and 21 is 126.

2. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

3. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 18 and 21?

Answer:

Least Common Multiple of 18 and 21 = 126

Step 1: Find the prime factorization of 18

18 = 2 x 3 x 3

Step 2: Find the prime factorization of 21

21 = 3 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 126 = 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 18 and 21 is 126.