Least Common Multiple of 678 and 684

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 678 and 684 the smallest integer that is 77292 that is divisible by both numbers.

Least Common Multiple (LCM) of 678 and 684 is 77292.

LCM(678,684) = 77292

LCM of 678 and 684

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

LCM of:
and

Least Common Multiple of 678 and 684

LCM of 678 and 684 is 77292

Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 684. First we will calculate the prime factors of 678 and 684.

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

Prime Factorization of 684


2 684
2 342
3 171
3 57
19 19
1

Prime factors of 684 are 2, 3,19. Prime factorization of 684 in exponential form is:

684 = 22×32×191

Now multiplying the highest exponent prime factors to calculate the LCM of 678 and 684.

LCM(678,684) = 22×32×191×1131
LCM(678,684) = 77292

Factors of 678

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

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

Factors of 684

List of positive integer factors of 684 that divides 684 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

Least Common Multiple of 678 and 684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 678 and 684, than apply into the LCM equation.

GCF(678,684) = 6
LCM(678,684) = ( 678 × 684) / 6
LCM(678,684) = 463752 / 6
LCM(678,684) = 77292

Properties of LCM 678 and 684

(i) The LCM of 684 and 678 is associative

LCM of 678 and 684 = LCM of 684 and 678

Related Least Common Multiples of 678

Related Least Common Multiples of 684

Frequently Asked Questions on LCM of 678 and 684

1. What is the LCM of 678 and 684?

Answer: LCM of 678 and 684 is 77292.

2. 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.

3. What are the Factors of 684?

Answer: Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. There are 18 integers that are factors of 684. The greatest factor of 684 is 684.

4. How to Find the LCM of 678 and 684?

Answer:

Least Common Multiple of 678 and 684 = 77292

Step 1: Find the prime factorization of 678

678 = 2 x 3 x 113

Step 2: Find the prime factorization of 684

684 = 2 x 2 x 3 x 3 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 = 77292 = 2 x 2 x 3 x 3 x 19 x 113

Step 4: Therefore, the least common multiple of 678 and 684 is 77292.