Least Common Multiple of 672 and 680

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 680 the smallest integer that is 57120 that is divisible by both numbers.

Least Common Multiple (LCM) of 672 and 680 is 57120.

LCM(672,680) = 57120

LCM of 672 and 680

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

LCM of:
and

Least Common Multiple of 672 and 680

LCM of 672 and 680 is 57120

Least common multiple can be found by multiplying the highest exponent prime factors of 672 and 680. First we will calculate the prime factors of 672 and 680.

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 680


2 680
2 340
2 170
5 85
17 17
1

Prime factors of 680 are 2, 5,17. Prime factorization of 680 in exponential form is:

680 = 23×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 672 and 680.

LCM(672,680) = 25×31×51×71×171
LCM(672,680) = 57120

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 680

List of positive integer factors of 680 that divides 680 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

Least Common Multiple of 672 and 680 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 680, than apply into the LCM equation.

GCF(672,680) = 8
LCM(672,680) = ( 672 × 680) / 8
LCM(672,680) = 456960 / 8
LCM(672,680) = 57120

Properties of LCM 672 and 680

(i) The LCM of 680 and 672 is associative

LCM of 672 and 680 = LCM of 680 and 672

Related Least Common Multiples of 672

Related Least Common Multiples of 680

Frequently Asked Questions on LCM of 672 and 680

1. What is the LCM of 672 and 680?

Answer: LCM of 672 and 680 is 57120.

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 680?

Answer: Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680. There are 16 integers that are factors of 680. The greatest factor of 680 is 680.

4. How to Find the LCM of 672 and 680?

Answer:

Least Common Multiple of 672 and 680 = 57120

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 680

680 = 2 x 2 x 2 x 5 x 17

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

LCM = 57120 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 672 and 680 is 57120.