Least Common Multiple of 6972 and 6976

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6972 and 6976 the smallest integer that is 12159168 that is divisible by both numbers.

Least Common Multiple (LCM) of 6972 and 6976 is 12159168.

LCM(6972,6976) = 12159168

LCM of 6972 and 6976

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

LCM of:
and

Least Common Multiple of 6972 and 6976

LCM of 6972 and 6976 is 12159168

Least common multiple can be found by multiplying the highest exponent prime factors of 6972 and 6976. First we will calculate the prime factors of 6972 and 6976.

Prime Factorization of 6972


2 6972
2 3486
3 1743
7 581
83 83
1

Prime factors of 6972 are 2, 3, 7,83. Prime factorization of 6972 in exponential form is:

6972 = 22×31×71×831

Prime Factorization of 6976


2 6976
2 3488
2 1744
2 872
2 436
2 218
109 109
1

Prime factors of 6976 are 2,109. Prime factorization of 6976 in exponential form is:

6976 = 26×1091

Now multiplying the highest exponent prime factors to calculate the LCM of 6972 and 6976.

LCM(6972,6976) = 26×31×71×831×1091
LCM(6972,6976) = 12159168

Factors of 6972

List of positive integer factors of 6972 that divides 6972 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486, 6972

Factors of 6976

List of positive integer factors of 6976 that divides 6976 without a remainder.

1, 2, 4, 8, 16, 32, 64, 109, 218, 436, 872, 1744, 3488, 6976

Least Common Multiple of 6972 and 6976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6972 and 6976, than apply into the LCM equation.

GCF(6972,6976) = 4
LCM(6972,6976) = ( 6972 × 6976) / 4
LCM(6972,6976) = 48636672 / 4
LCM(6972,6976) = 12159168

Properties of LCM 6972 and 6976

(i) The LCM of 6976 and 6972 is associative

LCM of 6972 and 6976 = LCM of 6976 and 6972

Related Least Common Multiples of 6972

Related Least Common Multiples of 6976

Frequently Asked Questions on LCM of 6972 and 6976

1. What is the LCM of 6972 and 6976?

Answer: LCM of 6972 and 6976 is 12159168.

2. What are the Factors of 6972?

Answer: Factors of 6972 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486, 6972. There are 24 integers that are factors of 6972. The greatest factor of 6972 is 6972.

3. What are the Factors of 6976?

Answer: Factors of 6976 are 1, 2, 4, 8, 16, 32, 64, 109, 218, 436, 872, 1744, 3488, 6976. There are 14 integers that are factors of 6976. The greatest factor of 6976 is 6976.

4. How to Find the LCM of 6972 and 6976?

Answer:

Least Common Multiple of 6972 and 6976 = 12159168

Step 1: Find the prime factorization of 6972

6972 = 2 x 2 x 3 x 7 x 83

Step 2: Find the prime factorization of 6976

6976 = 2 x 2 x 2 x 2 x 2 x 2 x 109

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

LCM = 12159168 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 83 x 109

Step 4: Therefore, the least common multiple of 6972 and 6976 is 12159168.