Least Common Multiple of 21 and 31

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 31 the smallest integer that is 651 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 31 is 651.

LCM(21,31) = 651

LCM of 21 and 31

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

LCM of:
and

Least Common Multiple of 21 and 31

LCM of 21 and 31 is 651

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 31. First we will calculate the prime factors of 21 and 31.

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 31


31 31
1

Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:

31 = 311

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 31.

LCM(21,31) = 31×71×311
LCM(21,31) = 651

Factors of 21

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

1, 3, 7, 21

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1, 31

Least Common Multiple of 21 and 31 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 31, than apply into the LCM equation.

GCF(21,31) = 1
LCM(21,31) = ( 21 × 31) / 1
LCM(21,31) = 651 / 1
LCM(21,31) = 651

Properties of LCM 21 and 31

(i) The LCM of 31 and 21 is associative

LCM of 21 and 31 = LCM of 31 and 21

Frequently Asked Questions on LCM of 21 and 31

1. What is the LCM of 21 and 31?

Answer: LCM of 21 and 31 is 651.

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 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

4. How to Find the LCM of 21 and 31?

Answer:

Least Common Multiple of 21 and 31 = 651

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 31

31 = 31

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

LCM = 651 = 3 x 7 x 31

Step 4: Therefore, the least common multiple of 21 and 31 is 651.