Least Common Multiple of 675 and 678

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 675 and 678 the smallest integer that is 152550 that is divisible by both numbers.

Least Common Multiple (LCM) of 675 and 678 is 152550.

LCM(675,678) = 152550

LCM of 675 and 678

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

LCM of:
and

Least Common Multiple of 675 and 678

LCM of 675 and 678 is 152550

Least common multiple can be found by multiplying the highest exponent prime factors of 675 and 678. First we will calculate the prime factors of 675 and 678.

Prime Factorization of 675


3 675
3 225
3 75
5 25
5 5
1

Prime factors of 675 are 3,5. Prime factorization of 675 in exponential form is:

675 = 33×52

Prime Factorization of 678


2 678
3 339
113 113
1

Prime factors of 678 are 2, 3,113. Prime factorization of 678 in exponential form is:

678 = 21×31×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 675 and 678.

LCM(675,678) = 21×33×52×1131
LCM(675,678) = 152550

Factors of 675

List of positive integer factors of 675 that divides 675 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

Factors of 678

List of positive integer factors of 678 that divides 678 without a remainder.

1, 2, 3, 6, 113, 226, 339, 678

Least Common Multiple of 675 and 678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 675 and 678, than apply into the LCM equation.

GCF(675,678) = 3
LCM(675,678) = ( 675 × 678) / 3
LCM(675,678) = 457650 / 3
LCM(675,678) = 152550

Properties of LCM 675 and 678

(i) The LCM of 678 and 675 is associative

LCM of 675 and 678 = LCM of 678 and 675

Related Least Common Multiples of 675

Related Least Common Multiples of 678

Frequently Asked Questions on LCM of 675 and 678

1. What is the LCM of 675 and 678?

Answer: LCM of 675 and 678 is 152550.

2. What are the Factors of 675?

Answer: Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675. There are 12 integers that are factors of 675. The greatest factor of 675 is 675.

3. What are the Factors of 678?

Answer: Factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678. There are 8 integers that are factors of 678. The greatest factor of 678 is 678.

4. How to Find the LCM of 675 and 678?

Answer:

Least Common Multiple of 675 and 678 = 152550

Step 1: Find the prime factorization of 675

675 = 3 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 678

678 = 2 x 3 x 113

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

LCM = 152550 = 2 x 3 x 3 x 3 x 5 x 5 x 113

Step 4: Therefore, the least common multiple of 675 and 678 is 152550.