Least Common Multiple of 966 and 972

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 966 and 972 the smallest integer that is 156492 that is divisible by both numbers.

Least Common Multiple (LCM) of 966 and 972 is 156492.

LCM(966,972) = 156492

LCM of 966 and 972

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

LCM of:
and

Least Common Multiple of 966 and 972

LCM of 966 and 972 is 156492

Least common multiple can be found by multiplying the highest exponent prime factors of 966 and 972. First we will calculate the prime factors of 966 and 972.

Prime Factorization of 966


2 966
3 483
7 161
23 23
1

Prime factors of 966 are 2, 3, 7,23. Prime factorization of 966 in exponential form is:

966 = 21×31×71×231

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

Now multiplying the highest exponent prime factors to calculate the LCM of 966 and 972.

LCM(966,972) = 22×35×71×231
LCM(966,972) = 156492

Factors of 966

List of positive integer factors of 966 that divides 966 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966

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

Least Common Multiple of 966 and 972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 966 and 972, than apply into the LCM equation.

GCF(966,972) = 6
LCM(966,972) = ( 966 × 972) / 6
LCM(966,972) = 938952 / 6
LCM(966,972) = 156492

Properties of LCM 966 and 972

(i) The LCM of 972 and 966 is associative

LCM of 966 and 972 = LCM of 972 and 966

Related Least Common Multiples of 966

Related Least Common Multiples of 972

Frequently Asked Questions on LCM of 966 and 972

1. What is the LCM of 966 and 972?

Answer: LCM of 966 and 972 is 156492.

2. What are the Factors of 966?

Answer: Factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966. There are 16 integers that are factors of 966. The greatest factor of 966 is 966.

3. 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.

4. How to Find the LCM of 966 and 972?

Answer:

Least Common Multiple of 966 and 972 = 156492

Step 1: Find the prime factorization of 966

966 = 2 x 3 x 7 x 23

Step 2: Find the prime factorization of 972

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

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

LCM = 156492 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 7 x 23

Step 4: Therefore, the least common multiple of 966 and 972 is 156492.