Least Common Multiple of 2970 and 2976

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2970 and 2976 the smallest integer that is 1473120 that is divisible by both numbers.

Least Common Multiple (LCM) of 2970 and 2976 is 1473120.

LCM(2970,2976) = 1473120

LCM of 2970 and 2976

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

LCM of:
and

Least Common Multiple of 2970 and 2976

LCM of 2970 and 2976 is 1473120

Least common multiple can be found by multiplying the highest exponent prime factors of 2970 and 2976. First we will calculate the prime factors of 2970 and 2976.

Prime Factorization of 2970


2 2970
3 1485
3 495
3 165
5 55
11 11
1

Prime factors of 2970 are 2, 3, 5,11. Prime factorization of 2970 in exponential form is:

2970 = 21×33×51×111

Prime Factorization of 2976


2 2976
2 1488
2 744
2 372
2 186
3 93
31 31
1

Prime factors of 2976 are 2, 3,31. Prime factorization of 2976 in exponential form is:

2976 = 25×31×311

Now multiplying the highest exponent prime factors to calculate the LCM of 2970 and 2976.

LCM(2970,2976) = 25×33×51×111×311
LCM(2970,2976) = 1473120

Factors of 2970

List of positive integer factors of 2970 that divides 2970 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 90, 99, 110, 135, 165, 198, 270, 297, 330, 495, 594, 990, 1485, 2970

Factors of 2976

List of positive integer factors of 2976 that divides 2976 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 93, 96, 124, 186, 248, 372, 496, 744, 992, 1488, 2976

Least Common Multiple of 2970 and 2976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2970 and 2976, than apply into the LCM equation.

GCF(2970,2976) = 6
LCM(2970,2976) = ( 2970 × 2976) / 6
LCM(2970,2976) = 8838720 / 6
LCM(2970,2976) = 1473120

Properties of LCM 2970 and 2976

(i) The LCM of 2976 and 2970 is associative

LCM of 2970 and 2976 = LCM of 2976 and 2970

Related Least Common Multiples of 2970

Related Least Common Multiples of 2976

Frequently Asked Questions on LCM of 2970 and 2976

1. What is the LCM of 2970 and 2976?

Answer: LCM of 2970 and 2976 is 1473120.

2. What are the Factors of 2970?

Answer: Factors of 2970 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 90, 99, 110, 135, 165, 198, 270, 297, 330, 495, 594, 990, 1485, 2970. There are 32 integers that are factors of 2970. The greatest factor of 2970 is 2970.

3. What are the Factors of 2976?

Answer: Factors of 2976 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 93, 96, 124, 186, 248, 372, 496, 744, 992, 1488, 2976. There are 24 integers that are factors of 2976. The greatest factor of 2976 is 2976.

4. How to Find the LCM of 2970 and 2976?

Answer:

Least Common Multiple of 2970 and 2976 = 1473120

Step 1: Find the prime factorization of 2970

2970 = 2 x 3 x 3 x 3 x 5 x 11

Step 2: Find the prime factorization of 2976

2976 = 2 x 2 x 2 x 2 x 2 x 3 x 31

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

LCM = 1473120 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 11 x 31

Step 4: Therefore, the least common multiple of 2970 and 2976 is 1473120.