Least Common Multiple of 972 and 974

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 974 the smallest integer that is 473364 that is divisible by both numbers.

Least Common Multiple (LCM) of 972 and 974 is 473364.

LCM(972,974) = 473364

LCM of 972 and 974

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

LCM of:
and

Least Common Multiple of 972 and 974

LCM of 972 and 974 is 473364

Least common multiple can be found by multiplying the highest exponent prime factors of 972 and 974. First we will calculate the prime factors of 972 and 974.

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 974


2 974
487 487
1

Prime factors of 974 are 2,487. Prime factorization of 974 in exponential form is:

974 = 21×4871

Now multiplying the highest exponent prime factors to calculate the LCM of 972 and 974.

LCM(972,974) = 22×35×4871
LCM(972,974) = 473364

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 974

List of positive integer factors of 974 that divides 974 without a remainder.

1, 2, 487, 974

Least Common Multiple of 972 and 974 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 974, than apply into the LCM equation.

GCF(972,974) = 2
LCM(972,974) = ( 972 × 974) / 2
LCM(972,974) = 946728 / 2
LCM(972,974) = 473364

Properties of LCM 972 and 974

(i) The LCM of 974 and 972 is associative

LCM of 972 and 974 = LCM of 974 and 972

Related Least Common Multiples of 972

Related Least Common Multiples of 974

Frequently Asked Questions on LCM of 972 and 974

1. What is the LCM of 972 and 974?

Answer: LCM of 972 and 974 is 473364.

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 974?

Answer: Factors of 974 are 1, 2, 487, 974. There are 4 integers that are factors of 974. The greatest factor of 974 is 974.

4. How to Find the LCM of 972 and 974?

Answer:

Least Common Multiple of 972 and 974 = 473364

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 974

974 = 2 x 487

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

LCM = 473364 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 487

Step 4: Therefore, the least common multiple of 972 and 974 is 473364.