Least Common Multiple of 972 and 976

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 976 the smallest integer that is 237168 that is divisible by both numbers.

Least Common Multiple (LCM) of 972 and 976 is 237168.

LCM(972,976) = 237168

LCM of 972 and 976

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

LCM of:
and

Least Common Multiple of 972 and 976

LCM of 972 and 976 is 237168

Least common multiple can be found by multiplying the highest exponent prime factors of 972 and 976. First we will calculate the prime factors of 972 and 976.

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 976


2 976
2 488
2 244
2 122
61 61
1

Prime factors of 976 are 2,61. Prime factorization of 976 in exponential form is:

976 = 24×611

Now multiplying the highest exponent prime factors to calculate the LCM of 972 and 976.

LCM(972,976) = 24×35×611
LCM(972,976) = 237168

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 976

List of positive integer factors of 976 that divides 976 without a remainder.

1, 2, 4, 8, 16, 61, 122, 244, 488, 976

Least Common Multiple of 972 and 976 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 976, than apply into the LCM equation.

GCF(972,976) = 4
LCM(972,976) = ( 972 × 976) / 4
LCM(972,976) = 948672 / 4
LCM(972,976) = 237168

Properties of LCM 972 and 976

(i) The LCM of 976 and 972 is associative

LCM of 972 and 976 = LCM of 976 and 972

Related Least Common Multiples of 972

Related Least Common Multiples of 976

Frequently Asked Questions on LCM of 972 and 976

1. What is the LCM of 972 and 976?

Answer: LCM of 972 and 976 is 237168.

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 976?

Answer: Factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976. There are 10 integers that are factors of 976. The greatest factor of 976 is 976.

4. How to Find the LCM of 972 and 976?

Answer:

Least Common Multiple of 972 and 976 = 237168

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 976

976 = 2 x 2 x 2 x 2 x 61

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

LCM = 237168 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 61

Step 4: Therefore, the least common multiple of 972 and 976 is 237168.