Least Common Multiple of 72 and 84

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 72 and 84 the smallest integer that is 504 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 84 is 504.

LCM(72,84) = 504

LCM of 72 and 84

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

LCM of:
and

Least Common Multiple of 72 and 84

LCM of 72 and 84 is 504

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 84. First we will calculate the prime factors of 72 and 84.

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

Prime Factorization of 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 84.

LCM(72,84) = 23×32×71
LCM(72,84) = 504

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Least Common Multiple of 72 and 84 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 84, than apply into the LCM equation.

GCF(72,84) = 12
LCM(72,84) = ( 72 × 84) / 12
LCM(72,84) = 6048 / 12
LCM(72,84) = 504

Properties of LCM 72 and 84

(i) The LCM of 84 and 72 is associative

LCM of 72 and 84 = LCM of 84 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 84

Frequently Asked Questions on LCM of 72 and 84

1. What is the LCM of 72 and 84?

Answer: LCM of 72 and 84 is 504.

2. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

3. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

4. How to Find the LCM of 72 and 84?

Answer:

Least Common Multiple of 72 and 84 = 504

Step 1: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 84

84 = 2 x 2 x 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 = 504 = 2 x 2 x 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 72 and 84 is 504.