Least Common Multiple of 21 and 30

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 30 the smallest integer that is 210 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 30 is 210.

LCM(21,30) = 210

LCM of 21 and 30

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

LCM of:
and

Least Common Multiple of 21 and 30

LCM of 21 and 30 is 210

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 30. First we will calculate the prime factors of 21 and 30.

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 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 30.

LCM(21,30) = 21×31×51×71
LCM(21,30) = 210

Factors of 21

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

1, 3, 7, 21

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Least Common Multiple of 21 and 30 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 30, than apply into the LCM equation.

GCF(21,30) = 3
LCM(21,30) = ( 21 × 30) / 3
LCM(21,30) = 630 / 3
LCM(21,30) = 210

Properties of LCM 21 and 30

(i) The LCM of 30 and 21 is associative

LCM of 21 and 30 = LCM of 30 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 30

Frequently Asked Questions on LCM of 21 and 30

1. What is the LCM of 21 and 30?

Answer: LCM of 21 and 30 is 210.

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 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the LCM of 21 and 30?

Answer:

Least Common Multiple of 21 and 30 = 210

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 30

30 = 2 x 3 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 = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 21 and 30 is 210.