Least Common Multiple of 9971 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 9971 and 9975 the smallest integer that is 99460725 that is divisible by both numbers.

Least Common Multiple (LCM) of 9971 and 9975 is 99460725.

LCM(9971,9975) = 99460725

LCM of 9971 and 9975

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

LCM of:
and

Least Common Multiple of 9971 and 9975

LCM of 9971 and 9975 is 99460725

Least common multiple can be found by multiplying the highest exponent prime factors of 9971 and 9975. First we will calculate the prime factors of 9971 and 9975.

Prime Factorization of 9971


13 9971
13 767
59 59
1

Prime factors of 9971 are 13,59. Prime factorization of 9971 in exponential form is:

9971 = 132×591

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 9971 and 9975.

LCM(9971,9975) = 31×52×71×132×191×591
LCM(9971,9975) = 99460725

Factors of 9971

List of positive integer factors of 9971 that divides 9971 without a remainder.

1, 13, 59, 169, 767, 9971

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 9971 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 9971 and 9975, than apply into the LCM equation.

GCF(9971,9975) = 1
LCM(9971,9975) = ( 9971 × 9975) / 1
LCM(9971,9975) = 99460725 / 1
LCM(9971,9975) = 99460725

Properties of LCM 9971 and 9975

(i) The LCM of 9975 and 9971 is associative

LCM of 9971 and 9975 = LCM of 9975 and 9971

Related Least Common Multiples of 9971

Related Least Common Multiples of 9975

Frequently Asked Questions on LCM of 9971 and 9975

1. What is the LCM of 9971 and 9975?

Answer: LCM of 9971 and 9975 is 99460725.

2. What are the Factors of 9971?

Answer: Factors of 9971 are 1, 13, 59, 169, 767, 9971. There are 6 integers that are factors of 9971. The greatest factor of 9971 is 9971.

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 9971 and 9975?

Answer:

Least Common Multiple of 9971 and 9975 = 99460725

Step 1: Find the prime factorization of 9971

9971 = 13 x 13 x 59

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 = 99460725 = 3 x 5 x 5 x 7 x 13 x 13 x 19 x 59

Step 4: Therefore, the least common multiple of 9971 and 9975 is 99460725.