Least Common Multiple of 72 and 76

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 76 the smallest integer that is 1368 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 76 is 1368.

LCM(72,76) = 1368

LCM of 72 and 76

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

LCM of:
and

Least Common Multiple of 72 and 76

LCM of 72 and 76 is 1368

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 76. First we will calculate the prime factors of 72 and 76.

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 76


2 76
2 38
19 19
1

Prime factors of 76 are 2,19. Prime factorization of 76 in exponential form is:

76 = 22×191

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 76.

LCM(72,76) = 23×32×191
LCM(72,76) = 1368

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 76

List of positive integer factors of 76 that divides 76 without a remainder.

1, 2, 4, 19, 38, 76

Least Common Multiple of 72 and 76 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 76, than apply into the LCM equation.

GCF(72,76) = 4
LCM(72,76) = ( 72 × 76) / 4
LCM(72,76) = 5472 / 4
LCM(72,76) = 1368

Properties of LCM 72 and 76

(i) The LCM of 76 and 72 is associative

LCM of 72 and 76 = LCM of 76 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 76

Frequently Asked Questions on LCM of 72 and 76

1. What is the LCM of 72 and 76?

Answer: LCM of 72 and 76 is 1368.

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 76?

Answer: Factors of 76 are 1, 2, 4, 19, 38, 76. There are 6 integers that are factors of 76. The greatest factor of 76 is 76.

4. How to Find the LCM of 72 and 76?

Answer:

Least Common Multiple of 72 and 76 = 1368

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 76

76 = 2 x 2 x 19

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

LCM = 1368 = 2 x 2 x 2 x 3 x 3 x 19

Step 4: Therefore, the least common multiple of 72 and 76 is 1368.