Least Common Multiple of 72 and 91

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 91 the smallest integer that is 6552 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 91 is 6552.

LCM(72,91) = 6552

LCM of 72 and 91

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

LCM of:
and

Least Common Multiple of 72 and 91

LCM of 72 and 91 is 6552

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 91. First we will calculate the prime factors of 72 and 91.

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 91


7 91
13 13
1

Prime factors of 91 are 7,13. Prime factorization of 91 in exponential form is:

91 = 71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 91.

LCM(72,91) = 23×32×71×131
LCM(72,91) = 6552

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 91

List of positive integer factors of 91 that divides 91 without a remainder.

1, 7, 13, 91

Least Common Multiple of 72 and 91 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 91, than apply into the LCM equation.

GCF(72,91) = 1
LCM(72,91) = ( 72 × 91) / 1
LCM(72,91) = 6552 / 1
LCM(72,91) = 6552

Properties of LCM 72 and 91

(i) The LCM of 91 and 72 is associative

LCM of 72 and 91 = LCM of 91 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 91

Frequently Asked Questions on LCM of 72 and 91

1. What is the LCM of 72 and 91?

Answer: LCM of 72 and 91 is 6552.

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 91?

Answer: Factors of 91 are 1, 7, 13, 91. There are 4 integers that are factors of 91. The greatest factor of 91 is 91.

4. How to Find the LCM of 72 and 91?

Answer:

Least Common Multiple of 72 and 91 = 6552

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 91

91 = 7 x 13

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

LCM = 6552 = 2 x 2 x 2 x 3 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 72 and 91 is 6552.