Least Common Multiple of 4 and 21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 4 and 21 the smallest integer that is 84 that is divisible by both numbers.

Least Common Multiple (LCM) of 4 and 21 is 84.

LCM(4,21) = 84

LCM of 4 and 21

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

LCM of:
and

Least Common Multiple of 4 and 21

LCM of 4 and 21 is 84

Least common multiple can be found by multiplying the highest exponent prime factors of 4 and 21. First we will calculate the prime factors of 4 and 21.

Prime Factorization of 4


2 4
2 2
1

Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:

4 = 22

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

Now multiplying the highest exponent prime factors to calculate the LCM of 4 and 21.

LCM(4,21) = 22×31×71
LCM(4,21) = 84

Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1, 2, 4

Factors of 21

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

1, 3, 7, 21

Least Common Multiple of 4 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4 and 21, than apply into the LCM equation.

GCF(4,21) = 1
LCM(4,21) = ( 4 × 21) / 1
LCM(4,21) = 84 / 1
LCM(4,21) = 84

Properties of LCM 4 and 21

(i) The LCM of 21 and 4 is associative

LCM of 4 and 21 = LCM of 21 and 4

Frequently Asked Questions on LCM of 4 and 21

1. What is the LCM of 4 and 21?

Answer: LCM of 4 and 21 is 84.

2. What are the Factors of 4?

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

3. 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.

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

Answer:

Least Common Multiple of 4 and 21 = 84

Step 1: Find the prime factorization of 4

4 = 2 x 2

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 84 = 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 4 and 21 is 84.