Least Common Multiple of 9972 and 9975

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 9975 the smallest integer that is 33156900 that is divisible by both numbers.

Least Common Multiple (LCM) of 9972 and 9975 is 33156900.

LCM(9972,9975) = 33156900

LCM of 9972 and 9975

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

LCM of:
and

Least Common Multiple of 9972 and 9975

LCM of 9972 and 9975 is 33156900

Least common multiple can be found by multiplying the highest exponent prime factors of 9972 and 9975. First we will calculate the prime factors of 9972 and 9975.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 9972 and 9975.

LCM(9972,9975) = 22×32×52×71×191×2771
LCM(9972,9975) = 33156900

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 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

Least Common Multiple of 9972 and 9975 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 9975, than apply into the LCM equation.

GCF(9972,9975) = 3
LCM(9972,9975) = ( 9972 × 9975) / 3
LCM(9972,9975) = 99470700 / 3
LCM(9972,9975) = 33156900

Properties of LCM 9972 and 9975

(i) The LCM of 9975 and 9972 is associative

LCM of 9972 and 9975 = LCM of 9975 and 9972

Related Least Common Multiples of 9972

Related Least Common Multiples of 9975

Frequently Asked Questions on LCM of 9972 and 9975

1. What is the LCM of 9972 and 9975?

Answer: LCM of 9972 and 9975 is 33156900.

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 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.

4. How to Find the LCM of 9972 and 9975?

Answer:

Least Common Multiple of 9972 and 9975 = 33156900

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 9975

9975 = 3 x 5 x 5 x 7 x 19

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

LCM = 33156900 = 2 x 2 x 3 x 3 x 5 x 5 x 7 x 19 x 277

Step 4: Therefore, the least common multiple of 9972 and 9975 is 33156900.