Least Common Multiple of 9975 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 9975 and 9980 the smallest integer that is 19910100 that is divisible by both numbers.

Least Common Multiple (LCM) of 9975 and 9980 is 19910100.

LCM(9975,9980) = 19910100

LCM of 9975 and 9980

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

LCM of:
and

Least Common Multiple of 9975 and 9980

LCM of 9975 and 9980 is 19910100

Least common multiple can be found by multiplying the highest exponent prime factors of 9975 and 9980. First we will calculate the prime factors of 9975 and 9980.

Prime Factorization of 9975


3 9975
5 3325
5 665
7 133
19 19
1

Prime factors of 9975 are 3, 5, 7,19. Prime factorization of 9975 in exponential form is:

9975 = 31×52×71×191

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 9975 and 9980.

LCM(9975,9980) = 22×31×52×71×191×4991
LCM(9975,9980) = 19910100

Factors of 9975

List of positive integer factors of 9975 that divides 9975 without a remainder.

1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975

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 9975 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 9975 and 9980, than apply into the LCM equation.

GCF(9975,9980) = 5
LCM(9975,9980) = ( 9975 × 9980) / 5
LCM(9975,9980) = 99550500 / 5
LCM(9975,9980) = 19910100

Properties of LCM 9975 and 9980

(i) The LCM of 9980 and 9975 is associative

LCM of 9975 and 9980 = LCM of 9980 and 9975

Related Least Common Multiples of 9975

Related Least Common Multiples of 9980

Frequently Asked Questions on LCM of 9975 and 9980

1. What is the LCM of 9975 and 9980?

Answer: LCM of 9975 and 9980 is 19910100.

2. What are the Factors of 9975?

Answer: Factors of 9975 are 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975. There are 24 integers that are factors of 9975. The greatest factor of 9975 is 9975.

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 9975 and 9980?

Answer:

Least Common Multiple of 9975 and 9980 = 19910100

Step 1: Find the prime factorization of 9975

9975 = 3 x 5 x 5 x 7 x 19

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 = 19910100 = 2 x 2 x 3 x 5 x 5 x 7 x 19 x 499

Step 4: Therefore, the least common multiple of 9975 and 9980 is 19910100.