Least Common Multiple of 9975 and 9978

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 9978 the smallest integer that is 33176850 that is divisible by both numbers.

Least Common Multiple (LCM) of 9975 and 9978 is 33176850.

LCM(9975,9978) = 33176850

LCM of 9975 and 9978

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

LCM of:
and

Least Common Multiple of 9975 and 9978

LCM of 9975 and 9978 is 33176850

Least common multiple can be found by multiplying the highest exponent prime factors of 9975 and 9978. First we will calculate the prime factors of 9975 and 9978.

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 9978


2 9978
3 4989
1663 1663
1

Prime factors of 9978 are 2, 3,1663. Prime factorization of 9978 in exponential form is:

9978 = 21×31×16631

Now multiplying the highest exponent prime factors to calculate the LCM of 9975 and 9978.

LCM(9975,9978) = 21×31×52×71×191×16631
LCM(9975,9978) = 33176850

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 9978

List of positive integer factors of 9978 that divides 9978 without a remainder.

1, 2, 3, 6, 1663, 3326, 4989, 9978

Least Common Multiple of 9975 and 9978 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 9978, than apply into the LCM equation.

GCF(9975,9978) = 3
LCM(9975,9978) = ( 9975 × 9978) / 3
LCM(9975,9978) = 99530550 / 3
LCM(9975,9978) = 33176850

Properties of LCM 9975 and 9978

(i) The LCM of 9978 and 9975 is associative

LCM of 9975 and 9978 = LCM of 9978 and 9975

Related Least Common Multiples of 9975

Related Least Common Multiples of 9978

Frequently Asked Questions on LCM of 9975 and 9978

1. What is the LCM of 9975 and 9978?

Answer: LCM of 9975 and 9978 is 33176850.

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 9978?

Answer: Factors of 9978 are 1, 2, 3, 6, 1663, 3326, 4989, 9978. There are 8 integers that are factors of 9978. The greatest factor of 9978 is 9978.

4. How to Find the LCM of 9975 and 9978?

Answer:

Least Common Multiple of 9975 and 9978 = 33176850

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 9978

9978 = 2 x 3 x 1663

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

LCM = 33176850 = 2 x 3 x 5 x 5 x 7 x 19 x 1663

Step 4: Therefore, the least common multiple of 9975 and 9978 is 33176850.