Least Common Multiple of 72 and 89

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 89 the smallest integer that is 6408 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 89 is 6408.

LCM(72,89) = 6408

LCM of 72 and 89

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

LCM of:
and

Least Common Multiple of 72 and 89

LCM of 72 and 89 is 6408

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 89. First we will calculate the prime factors of 72 and 89.

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 89


89 89
1

Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:

89 = 891

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 89.

LCM(72,89) = 23×32×891
LCM(72,89) = 6408

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 89

List of positive integer factors of 89 that divides 89 without a remainder.

1, 89

Least Common Multiple of 72 and 89 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 89, than apply into the LCM equation.

GCF(72,89) = 1
LCM(72,89) = ( 72 × 89) / 1
LCM(72,89) = 6408 / 1
LCM(72,89) = 6408

Properties of LCM 72 and 89

(i) The LCM of 89 and 72 is associative

LCM of 72 and 89 = LCM of 89 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 89

Frequently Asked Questions on LCM of 72 and 89

1. What is the LCM of 72 and 89?

Answer: LCM of 72 and 89 is 6408.

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 89?

Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.

4. How to Find the LCM of 72 and 89?

Answer:

Least Common Multiple of 72 and 89 = 6408

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 89

89 = 89

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

LCM = 6408 = 2 x 2 x 2 x 3 x 3 x 89

Step 4: Therefore, the least common multiple of 72 and 89 is 6408.