Least Common Multiple of 969 and 975

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 969 and 975 the smallest integer that is 314925 that is divisible by both numbers.

Least Common Multiple (LCM) of 969 and 975 is 314925.

LCM(969,975) = 314925

LCM of 969 and 975

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

LCM of:
and

Least Common Multiple of 969 and 975

LCM of 969 and 975 is 314925

Least common multiple can be found by multiplying the highest exponent prime factors of 969 and 975. First we will calculate the prime factors of 969 and 975.

Prime Factorization of 969


3 969
17 323
19 19
1

Prime factors of 969 are 3, 17,19. Prime factorization of 969 in exponential form is:

969 = 31×171×191

Prime Factorization of 975


3 975
5 325
5 65
13 13
1

Prime factors of 975 are 3, 5,13. Prime factorization of 975 in exponential form is:

975 = 31×52×131

Now multiplying the highest exponent prime factors to calculate the LCM of 969 and 975.

LCM(969,975) = 31×52×131×171×191
LCM(969,975) = 314925

Factors of 969

List of positive integer factors of 969 that divides 969 without a remainder.

1, 3, 17, 19, 51, 57, 323, 969

Factors of 975

List of positive integer factors of 975 that divides 975 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975

Least Common Multiple of 969 and 975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 969 and 975, than apply into the LCM equation.

GCF(969,975) = 3
LCM(969,975) = ( 969 × 975) / 3
LCM(969,975) = 944775 / 3
LCM(969,975) = 314925

Properties of LCM 969 and 975

(i) The LCM of 975 and 969 is associative

LCM of 969 and 975 = LCM of 975 and 969

Related Least Common Multiples of 969

Related Least Common Multiples of 975

Frequently Asked Questions on LCM of 969 and 975

1. What is the LCM of 969 and 975?

Answer: LCM of 969 and 975 is 314925.

2. What are the Factors of 969?

Answer: Factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969. There are 8 integers that are factors of 969. The greatest factor of 969 is 969.

3. What are the Factors of 975?

Answer: Factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975. There are 12 integers that are factors of 975. The greatest factor of 975 is 975.

4. How to Find the LCM of 969 and 975?

Answer:

Least Common Multiple of 969 and 975 = 314925

Step 1: Find the prime factorization of 969

969 = 3 x 17 x 19

Step 2: Find the prime factorization of 975

975 = 3 x 5 x 5 x 13

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

LCM = 314925 = 3 x 5 x 5 x 13 x 17 x 19

Step 4: Therefore, the least common multiple of 969 and 975 is 314925.