Least Common Multiple of 972 and 980

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 980 the smallest integer that is 238140 that is divisible by both numbers.

Least Common Multiple (LCM) of 972 and 980 is 238140.

LCM(972,980) = 238140

LCM of 972 and 980

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

LCM of:
and

Least Common Multiple of 972 and 980

LCM of 972 and 980 is 238140

Least common multiple can be found by multiplying the highest exponent prime factors of 972 and 980. First we will calculate the prime factors of 972 and 980.

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 980


2 980
2 490
5 245
7 49
7 7
1

Prime factors of 980 are 2, 5,7. Prime factorization of 980 in exponential form is:

980 = 22×51×72

Now multiplying the highest exponent prime factors to calculate the LCM of 972 and 980.

LCM(972,980) = 22×35×51×72
LCM(972,980) = 238140

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 980

List of positive integer factors of 980 that divides 980 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

Least Common Multiple of 972 and 980 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 980, than apply into the LCM equation.

GCF(972,980) = 4
LCM(972,980) = ( 972 × 980) / 4
LCM(972,980) = 952560 / 4
LCM(972,980) = 238140

Properties of LCM 972 and 980

(i) The LCM of 980 and 972 is associative

LCM of 972 and 980 = LCM of 980 and 972

Related Least Common Multiples of 972

Related Least Common Multiples of 980

Frequently Asked Questions on LCM of 972 and 980

1. What is the LCM of 972 and 980?

Answer: LCM of 972 and 980 is 238140.

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 980?

Answer: Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980. There are 18 integers that are factors of 980. The greatest factor of 980 is 980.

4. How to Find the LCM of 972 and 980?

Answer:

Least Common Multiple of 972 and 980 = 238140

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 980

980 = 2 x 2 x 5 x 7 x 7

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

LCM = 238140 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7

Step 4: Therefore, the least common multiple of 972 and 980 is 238140.