Least Common Multiple of 21 and 32

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 32 the smallest integer that is 672 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 32 is 672.

LCM(21,32) = 672

LCM of 21 and 32

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

LCM of:
and

Least Common Multiple of 21 and 32

LCM of 21 and 32 is 672

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 32. First we will calculate the prime factors of 21 and 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

Prime Factorization of 32


2 32
2 16
2 8
2 4
2 2
1

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 32.

LCM(21,32) = 25×31×71
LCM(21,32) = 672

Factors of 21

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

1, 3, 7, 21

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1, 2, 4, 8, 16, 32

Least Common Multiple of 21 and 32 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 32, than apply into the LCM equation.

GCF(21,32) = 1
LCM(21,32) = ( 21 × 32) / 1
LCM(21,32) = 672 / 1
LCM(21,32) = 672

Properties of LCM 21 and 32

(i) The LCM of 32 and 21 is associative

LCM of 21 and 32 = LCM of 32 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 32

Frequently Asked Questions on LCM of 21 and 32

1. What is the LCM of 21 and 32?

Answer: LCM of 21 and 32 is 672.

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 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

4. How to Find the LCM of 21 and 32?

Answer:

Least Common Multiple of 21 and 32 = 672

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

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

LCM = 672 = 2 x 2 x 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 21 and 32 is 672.