Least Common Multiple of 9972 and 9976

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9972 and 9976 the smallest integer that is 24870168 that is divisible by both numbers.

Least Common Multiple (LCM) of 9972 and 9976 is 24870168.

LCM(9972,9976) = 24870168

LCM of 9972 and 9976

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

LCM of:
and

Least Common Multiple of 9972 and 9976

LCM of 9972 and 9976 is 24870168

Least common multiple can be found by multiplying the highest exponent prime factors of 9972 and 9976. First we will calculate the prime factors of 9972 and 9976.

Prime Factorization of 9972


2 9972
2 4986
3 2493
3 831
277 277
1

Prime factors of 9972 are 2, 3,277. Prime factorization of 9972 in exponential form is:

9972 = 22×32×2771

Prime Factorization of 9976


2 9976
2 4988
2 2494
29 1247
43 43
1

Prime factors of 9976 are 2, 29,43. Prime factorization of 9976 in exponential form is:

9976 = 23×291×431

Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9976.

LCM(9972,9976) = 23×32×291×431×2771
LCM(9972,9976) = 24870168

Factors of 9972

List of positive integer factors of 9972 that divides 9972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972

Factors of 9976

List of positive integer factors of 9976 that divides 9976 without a remainder.

1, 2, 4, 8, 29, 43, 58, 86, 116, 172, 232, 344, 1247, 2494, 4988, 9976

Least Common Multiple of 9972 and 9976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9972 and 9976, than apply into the LCM equation.

GCF(9972,9976) = 4
LCM(9972,9976) = ( 9972 × 9976) / 4
LCM(9972,9976) = 99480672 / 4
LCM(9972,9976) = 24870168

Properties of LCM 9972 and 9976

(i) The LCM of 9976 and 9972 is associative

LCM of 9972 and 9976 = LCM of 9976 and 9972

Related Least Common Multiples of 9972

Related Least Common Multiples of 9976

Frequently Asked Questions on LCM of 9972 and 9976

1. What is the LCM of 9972 and 9976?

Answer: LCM of 9972 and 9976 is 24870168.

2. What are the Factors of 9972?

Answer: Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972. There are 18 integers that are factors of 9972. The greatest factor of 9972 is 9972.

3. What are the Factors of 9976?

Answer: Factors of 9976 are 1, 2, 4, 8, 29, 43, 58, 86, 116, 172, 232, 344, 1247, 2494, 4988, 9976. There are 16 integers that are factors of 9976. The greatest factor of 9976 is 9976.

4. How to Find the LCM of 9972 and 9976?

Answer:

Least Common Multiple of 9972 and 9976 = 24870168

Step 1: Find the prime factorization of 9972

9972 = 2 x 2 x 3 x 3 x 277

Step 2: Find the prime factorization of 9976

9976 = 2 x 2 x 2 x 29 x 43

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

LCM = 24870168 = 2 x 2 x 2 x 3 x 3 x 29 x 43 x 277

Step 4: Therefore, the least common multiple of 9972 and 9976 is 24870168.