Least Common Multiple of 21 and 40

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 40 the smallest integer that is 840 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 40 is 840.

LCM(21,40) = 840

LCM of 21 and 40

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

LCM of:
and

Least Common Multiple of 21 and 40

LCM of 21 and 40 is 840

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 40. First we will calculate the prime factors of 21 and 40.

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 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 40.

LCM(21,40) = 23×31×51×71
LCM(21,40) = 840

Factors of 21

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

1, 3, 7, 21

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

Least Common Multiple of 21 and 40 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 40, than apply into the LCM equation.

GCF(21,40) = 1
LCM(21,40) = ( 21 × 40) / 1
LCM(21,40) = 840 / 1
LCM(21,40) = 840

Properties of LCM 21 and 40

(i) The LCM of 40 and 21 is associative

LCM of 21 and 40 = LCM of 40 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 40

Frequently Asked Questions on LCM of 21 and 40

1. What is the LCM of 21 and 40?

Answer: LCM of 21 and 40 is 840.

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 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

4. How to Find the LCM of 21 and 40?

Answer:

Least Common Multiple of 21 and 40 = 840

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

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

LCM = 840 = 2 x 2 x 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 21 and 40 is 840.