Least Common Multiple of 72 and 87

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 87 the smallest integer that is 2088 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 87 is 2088.

LCM(72,87) = 2088

LCM of 72 and 87

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

LCM of:
and

Least Common Multiple of 72 and 87

LCM of 72 and 87 is 2088

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 87. First we will calculate the prime factors of 72 and 87.

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 87


3 87
29 29
1

Prime factors of 87 are 3,29. Prime factorization of 87 in exponential form is:

87 = 31×291

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 87.

LCM(72,87) = 23×32×291
LCM(72,87) = 2088

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 87

List of positive integer factors of 87 that divides 87 without a remainder.

1, 3, 29, 87

Least Common Multiple of 72 and 87 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 87, than apply into the LCM equation.

GCF(72,87) = 3
LCM(72,87) = ( 72 × 87) / 3
LCM(72,87) = 6264 / 3
LCM(72,87) = 2088

Properties of LCM 72 and 87

(i) The LCM of 87 and 72 is associative

LCM of 72 and 87 = LCM of 87 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 87

Frequently Asked Questions on LCM of 72 and 87

1. What is the LCM of 72 and 87?

Answer: LCM of 72 and 87 is 2088.

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 87?

Answer: Factors of 87 are 1, 3, 29, 87. There are 4 integers that are factors of 87. The greatest factor of 87 is 87.

4. How to Find the LCM of 72 and 87?

Answer:

Least Common Multiple of 72 and 87 = 2088

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 87

87 = 3 x 29

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

LCM = 2088 = 2 x 2 x 2 x 3 x 3 x 29

Step 4: Therefore, the least common multiple of 72 and 87 is 2088.