Least Common Multiple of 72 and 75

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 75 the smallest integer that is 1800 that is divisible by both numbers.

Least Common Multiple (LCM) of 72 and 75 is 1800.

LCM(72,75) = 1800

LCM of 72 and 75

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

LCM of:
and

Least Common Multiple of 72 and 75

LCM of 72 and 75 is 1800

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 75. First we will calculate the prime factors of 72 and 75.

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 75


3 75
5 25
5 5
1

Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:

75 = 31×52

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 75.

LCM(72,75) = 23×32×52
LCM(72,75) = 1800

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 75

List of positive integer factors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25, 75

Least Common Multiple of 72 and 75 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 75, than apply into the LCM equation.

GCF(72,75) = 3
LCM(72,75) = ( 72 × 75) / 3
LCM(72,75) = 5400 / 3
LCM(72,75) = 1800

Properties of LCM 72 and 75

(i) The LCM of 75 and 72 is associative

LCM of 72 and 75 = LCM of 75 and 72

Related Least Common Multiples of 72

Related Least Common Multiples of 75

Frequently Asked Questions on LCM of 72 and 75

1. What is the LCM of 72 and 75?

Answer: LCM of 72 and 75 is 1800.

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 75?

Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.

4. How to Find the LCM of 72 and 75?

Answer:

Least Common Multiple of 72 and 75 = 1800

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 75

75 = 3 x 5 x 5

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

LCM = 1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 72 and 75 is 1800.