Least Common Multiple of 9975 and 9981

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 9981 the smallest integer that is 33186825 that is divisible by both numbers.

Least Common Multiple (LCM) of 9975 and 9981 is 33186825.

LCM(9975,9981) = 33186825

LCM of 9975 and 9981

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

LCM of:
and

Least Common Multiple of 9975 and 9981

LCM of 9975 and 9981 is 33186825

Least common multiple can be found by multiplying the highest exponent prime factors of 9975 and 9981. First we will calculate the prime factors of 9975 and 9981.

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 9981


3 9981
3 3327
1109 1109
1

Prime factors of 9981 are 3,1109. Prime factorization of 9981 in exponential form is:

9981 = 32×11091

Now multiplying the highest exponent prime factors to calculate the LCM of 9975 and 9981.

LCM(9975,9981) = 32×52×71×191×11091
LCM(9975,9981) = 33186825

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 9981

List of positive integer factors of 9981 that divides 9981 without a remainder.

1, 3, 9, 1109, 3327, 9981

Least Common Multiple of 9975 and 9981 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 9981, than apply into the LCM equation.

GCF(9975,9981) = 3
LCM(9975,9981) = ( 9975 × 9981) / 3
LCM(9975,9981) = 99560475 / 3
LCM(9975,9981) = 33186825

Properties of LCM 9975 and 9981

(i) The LCM of 9981 and 9975 is associative

LCM of 9975 and 9981 = LCM of 9981 and 9975

Related Least Common Multiples of 9975

Related Least Common Multiples of 9981

Frequently Asked Questions on LCM of 9975 and 9981

1. What is the LCM of 9975 and 9981?

Answer: LCM of 9975 and 9981 is 33186825.

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 9981?

Answer: Factors of 9981 are 1, 3, 9, 1109, 3327, 9981. There are 6 integers that are factors of 9981. The greatest factor of 9981 is 9981.

4. How to Find the LCM of 9975 and 9981?

Answer:

Least Common Multiple of 9975 and 9981 = 33186825

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 9981

9981 = 3 x 3 x 1109

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

LCM = 33186825 = 3 x 3 x 5 x 5 x 7 x 19 x 1109

Step 4: Therefore, the least common multiple of 9975 and 9981 is 33186825.