Least Common Multiple of 972 and 975

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 972 and 975 the smallest integer that is 315900 that is divisible by both numbers.

Least Common Multiple (LCM) of 972 and 975 is 315900.

LCM(972,975) = 315900

LCM of 972 and 975

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

LCM of:
and

Least Common Multiple of 972 and 975

LCM of 972 and 975 is 315900

Least common multiple can be found by multiplying the highest exponent prime factors of 972 and 975. First we will calculate the prime factors of 972 and 975.

Prime Factorization of 972


2 972
2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 972 are 2,3. Prime factorization of 972 in exponential form is:

972 = 22×35

Prime Factorization of 975


3 975
5 325
5 65
13 13
1

Prime factors of 975 are 3, 5,13. Prime factorization of 975 in exponential form is:

975 = 31×52×131

Now multiplying the highest exponent prime factors to calculate the LCM of 972 and 975.

LCM(972,975) = 22×35×52×131
LCM(972,975) = 315900

Factors of 972

List of positive integer factors of 972 that divides 972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972

Factors of 975

List of positive integer factors of 975 that divides 975 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975

Least Common Multiple of 972 and 975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 972 and 975, than apply into the LCM equation.

GCF(972,975) = 3
LCM(972,975) = ( 972 × 975) / 3
LCM(972,975) = 947700 / 3
LCM(972,975) = 315900

Properties of LCM 972 and 975

(i) The LCM of 975 and 972 is associative

LCM of 972 and 975 = LCM of 975 and 972

Related Least Common Multiples of 972

Related Least Common Multiples of 975

Frequently Asked Questions on LCM of 972 and 975

1. What is the LCM of 972 and 975?

Answer: LCM of 972 and 975 is 315900.

2. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

3. What are the Factors of 975?

Answer: Factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975. There are 12 integers that are factors of 975. The greatest factor of 975 is 975.

4. How to Find the LCM of 972 and 975?

Answer:

Least Common Multiple of 972 and 975 = 315900

Step 1: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 975

975 = 3 x 5 x 5 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 = 315900 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 13

Step 4: Therefore, the least common multiple of 972 and 975 is 315900.