Least Common Multiple of 9969 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 9969 and 9975 the smallest integer that is 33146925 that is divisible by both numbers.

Least Common Multiple (LCM) of 9969 and 9975 is 33146925.

LCM(9969,9975) = 33146925

LCM of 9969 and 9975

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

LCM of:
and

Least Common Multiple of 9969 and 9975

LCM of 9969 and 9975 is 33146925

Least common multiple can be found by multiplying the highest exponent prime factors of 9969 and 9975. First we will calculate the prime factors of 9969 and 9975.

Prime Factorization of 9969


3 9969
3323 3323
1

Prime factors of 9969 are 3,3323. Prime factorization of 9969 in exponential form is:

9969 = 31×33231

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 9969 and 9975.

LCM(9969,9975) = 31×52×71×191×33231
LCM(9969,9975) = 33146925

Factors of 9969

List of positive integer factors of 9969 that divides 9969 without a remainder.

1, 3, 3323, 9969

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 9969 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 9969 and 9975, than apply into the LCM equation.

GCF(9969,9975) = 3
LCM(9969,9975) = ( 9969 × 9975) / 3
LCM(9969,9975) = 99440775 / 3
LCM(9969,9975) = 33146925

Properties of LCM 9969 and 9975

(i) The LCM of 9975 and 9969 is associative

LCM of 9969 and 9975 = LCM of 9975 and 9969

Related Least Common Multiples of 9969

Related Least Common Multiples of 9975

Frequently Asked Questions on LCM of 9969 and 9975

1. What is the LCM of 9969 and 9975?

Answer: LCM of 9969 and 9975 is 33146925.

2. What are the Factors of 9969?

Answer: Factors of 9969 are 1, 3, 3323, 9969. There are 4 integers that are factors of 9969. The greatest factor of 9969 is 9969.

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 9969 and 9975?

Answer:

Least Common Multiple of 9969 and 9975 = 33146925

Step 1: Find the prime factorization of 9969

9969 = 3 x 3323

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 = 33146925 = 3 x 5 x 5 x 7 x 19 x 3323

Step 4: Therefore, the least common multiple of 9969 and 9975 is 33146925.