Least Common Multiple of 678 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 678 and 680 the smallest integer that is 230520 that is divisible by both numbers.

Least Common Multiple (LCM) of 678 and 680 is 230520.

LCM(678,680) = 230520

LCM of 678 and 680

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

LCM of:
and

Least Common Multiple of 678 and 680

LCM of 678 and 680 is 230520

Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 680. First we will calculate the prime factors of 678 and 680.

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 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 678 and 680.

LCM(678,680) = 23×31×51×171×1131
LCM(678,680) = 230520

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 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 678 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 678 and 680, than apply into the LCM equation.

GCF(678,680) = 2
LCM(678,680) = ( 678 × 680) / 2
LCM(678,680) = 461040 / 2
LCM(678,680) = 230520

Properties of LCM 678 and 680

(i) The LCM of 680 and 678 is associative

LCM of 678 and 680 = LCM of 680 and 678

Related Least Common Multiples of 678

Related Least Common Multiples of 680

Frequently Asked Questions on LCM of 678 and 680

1. What is the LCM of 678 and 680?

Answer: LCM of 678 and 680 is 230520.

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 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 678 and 680?

Answer:

Least Common Multiple of 678 and 680 = 230520

Step 1: Find the prime factorization of 678

678 = 2 x 3 x 113

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 = 230520 = 2 x 2 x 2 x 3 x 5 x 17 x 113

Step 4: Therefore, the least common multiple of 678 and 680 is 230520.