Least Common Multiple of 672 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 672 and 678 the smallest integer that is 75936 that is divisible by both numbers.

Least Common Multiple (LCM) of 672 and 678 is 75936.

LCM(672,678) = 75936

LCM of 672 and 678

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

LCM of:
and

Least Common Multiple of 672 and 678

LCM of 672 and 678 is 75936

Least common multiple can be found by multiplying the highest exponent prime factors of 672 and 678. First we will calculate the prime factors of 672 and 678.

Prime Factorization of 672


2 672
2 336
2 168
2 84
2 42
3 21
7 7
1

Prime factors of 672 are 2, 3,7. Prime factorization of 672 in exponential form is:

672 = 25×31×71

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 672 and 678.

LCM(672,678) = 25×31×71×1131
LCM(672,678) = 75936

Factors of 672

List of positive integer factors of 672 that divides 672 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672

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 672 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 672 and 678, than apply into the LCM equation.

GCF(672,678) = 6
LCM(672,678) = ( 672 × 678) / 6
LCM(672,678) = 455616 / 6
LCM(672,678) = 75936

Properties of LCM 672 and 678

(i) The LCM of 678 and 672 is associative

LCM of 672 and 678 = LCM of 678 and 672

Related Least Common Multiples of 672

Related Least Common Multiples of 678

Frequently Asked Questions on LCM of 672 and 678

1. What is the LCM of 672 and 678?

Answer: LCM of 672 and 678 is 75936.

2. What are the Factors of 672?

Answer: Factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672. There are 24 integers that are factors of 672. The greatest factor of 672 is 672.

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 672 and 678?

Answer:

Least Common Multiple of 672 and 678 = 75936

Step 1: Find the prime factorization of 672

672 = 2 x 2 x 2 x 2 x 2 x 3 x 7

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 = 75936 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 113

Step 4: Therefore, the least common multiple of 672 and 678 is 75936.