Least Common Multiple of 975 and 978

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 975 and 978 the smallest integer that is 317850 that is divisible by both numbers.

Least Common Multiple (LCM) of 975 and 978 is 317850.

LCM(975,978) = 317850

LCM of 975 and 978

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

LCM of:
and

Least Common Multiple of 975 and 978

LCM of 975 and 978 is 317850

Least common multiple can be found by multiplying the highest exponent prime factors of 975 and 978. First we will calculate the prime factors of 975 and 978.

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

Prime Factorization of 978


2 978
3 489
163 163
1

Prime factors of 978 are 2, 3,163. Prime factorization of 978 in exponential form is:

978 = 21×31×1631

Now multiplying the highest exponent prime factors to calculate the LCM of 975 and 978.

LCM(975,978) = 21×31×52×131×1631
LCM(975,978) = 317850

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

Factors of 978

List of positive integer factors of 978 that divides 978 without a remainder.

1, 2, 3, 6, 163, 326, 489, 978

Least Common Multiple of 975 and 978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 975 and 978, than apply into the LCM equation.

GCF(975,978) = 3
LCM(975,978) = ( 975 × 978) / 3
LCM(975,978) = 953550 / 3
LCM(975,978) = 317850

Properties of LCM 975 and 978

(i) The LCM of 978 and 975 is associative

LCM of 975 and 978 = LCM of 978 and 975

Related Least Common Multiples of 975

Related Least Common Multiples of 978

Frequently Asked Questions on LCM of 975 and 978

1. What is the LCM of 975 and 978?

Answer: LCM of 975 and 978 is 317850.

2. 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.

3. What are the Factors of 978?

Answer: Factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978. There are 8 integers that are factors of 978. The greatest factor of 978 is 978.

4. How to Find the LCM of 975 and 978?

Answer:

Least Common Multiple of 975 and 978 = 317850

Step 1: Find the prime factorization of 975

975 = 3 x 5 x 5 x 13

Step 2: Find the prime factorization of 978

978 = 2 x 3 x 163

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

LCM = 317850 = 2 x 3 x 5 x 5 x 13 x 163

Step 4: Therefore, the least common multiple of 975 and 978 is 317850.