Least Common Multiple of 72 and 77

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 77 the smallest integer that is 5544 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 77 is 5544.

LCM(72,77) = 5544

LCM of 72 and 77

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

LCM of:
and

Least Common Multiple of 72 and 77

LCM of 72 and 77 is 5544

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 77. First we will calculate the prime factors of 72 and 77.

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 77


7 77
11 11
1

Prime factors of 77 are 7,11. Prime factorization of 77 in exponential form is:

77 = 71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 77.

LCM(72,77) = 23×32×71×111
LCM(72,77) = 5544

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 77

List of positive integer factors of 77 that divides 77 without a remainder.

1, 7, 11, 77

Least Common Multiple of 72 and 77 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 77, than apply into the LCM equation.

GCF(72,77) = 1
LCM(72,77) = ( 72 × 77) / 1
LCM(72,77) = 5544 / 1
LCM(72,77) = 5544

Properties of LCM 72 and 77

(i) The LCM of 77 and 72 is associative

LCM of 72 and 77 = LCM of 77 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 77

Frequently Asked Questions on LCM of 72 and 77

1. What is the LCM of 72 and 77?

Answer: LCM of 72 and 77 is 5544.

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 77?

Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.

4. How to Find the LCM of 72 and 77?

Answer:

Least Common Multiple of 72 and 77 = 5544

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 77

77 = 7 x 11

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

LCM = 5544 = 2 x 2 x 2 x 3 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 72 and 77 is 5544.