Least Common Multiple of 21 and 24

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 21 and 24 the smallest integer that is 168 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 24 is 168.

LCM(21,24) = 168

LCM of 21 and 24

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

LCM of:
and

Least Common Multiple of 21 and 24

LCM of 21 and 24 is 168

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 24. First we will calculate the prime factors of 21 and 24.

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

Prime Factorization of 24


2 24
2 12
2 6
3 3
1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:

24 = 23×31

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 24.

LCM(21,24) = 23×31×71
LCM(21,24) = 168

Factors of 21

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

1, 3, 7, 21

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24

Least Common Multiple of 21 and 24 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 24, than apply into the LCM equation.

GCF(21,24) = 3
LCM(21,24) = ( 21 × 24) / 3
LCM(21,24) = 504 / 3
LCM(21,24) = 168

Properties of LCM 21 and 24

(i) The LCM of 24 and 21 is associative

LCM of 21 and 24 = LCM of 24 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 24

Frequently Asked Questions on LCM of 21 and 24

1. What is the LCM of 21 and 24?

Answer: LCM of 21 and 24 is 168.

2. 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.

3. What are the Factors of 24?

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.

4. How to Find the LCM of 21 and 24?

Answer:

Least Common Multiple of 21 and 24 = 168

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

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

LCM = 168 = 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 21 and 24 is 168.