Least Common Multiple of 9972 and 9980

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 9980 the smallest integer that is 24880140 that is divisible by both numbers.

Least Common Multiple (LCM) of 9972 and 9980 is 24880140.

LCM(9972,9980) = 24880140

LCM of 9972 and 9980

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

LCM of:
and

Least Common Multiple of 9972 and 9980

LCM of 9972 and 9980 is 24880140

Least common multiple can be found by multiplying the highest exponent prime factors of 9972 and 9980. First we will calculate the prime factors of 9972 and 9980.

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 9980


2 9980
2 4990
5 2495
499 499
1

Prime factors of 9980 are 2, 5,499. Prime factorization of 9980 in exponential form is:

9980 = 22×51×4991

Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9980.

LCM(9972,9980) = 22×32×51×2771×4991
LCM(9972,9980) = 24880140

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 9980

List of positive integer factors of 9980 that divides 9980 without a remainder.

1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980

Least Common Multiple of 9972 and 9980 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 9980, than apply into the LCM equation.

GCF(9972,9980) = 4
LCM(9972,9980) = ( 9972 × 9980) / 4
LCM(9972,9980) = 99520560 / 4
LCM(9972,9980) = 24880140

Properties of LCM 9972 and 9980

(i) The LCM of 9980 and 9972 is associative

LCM of 9972 and 9980 = LCM of 9980 and 9972

Related Least Common Multiples of 9972

Related Least Common Multiples of 9980

Frequently Asked Questions on LCM of 9972 and 9980

1. What is the LCM of 9972 and 9980?

Answer: LCM of 9972 and 9980 is 24880140.

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 9980?

Answer: Factors of 9980 are 1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980. There are 12 integers that are factors of 9980. The greatest factor of 9980 is 9980.

4. How to Find the LCM of 9972 and 9980?

Answer:

Least Common Multiple of 9972 and 9980 = 24880140

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 9980

9980 = 2 x 2 x 5 x 499

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

LCM = 24880140 = 2 x 2 x 3 x 3 x 5 x 277 x 499

Step 4: Therefore, the least common multiple of 9972 and 9980 is 24880140.