Least Common Multiple of 680 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 680 and 684 the smallest integer that is 116280 that is divisible by both numbers.

Least Common Multiple (LCM) of 680 and 684 is 116280.

LCM(680,684) = 116280

LCM of 680 and 684

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

LCM of:
and

Least Common Multiple of 680 and 684

LCM of 680 and 684 is 116280

Least common multiple can be found by multiplying the highest exponent prime factors of 680 and 684. First we will calculate the prime factors of 680 and 684.

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

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 680 and 684.

LCM(680,684) = 23×32×51×171×191
LCM(680,684) = 116280

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

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 680 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 680 and 684, than apply into the LCM equation.

GCF(680,684) = 4
LCM(680,684) = ( 680 × 684) / 4
LCM(680,684) = 465120 / 4
LCM(680,684) = 116280

Properties of LCM 680 and 684

(i) The LCM of 684 and 680 is associative

LCM of 680 and 684 = LCM of 684 and 680

Related Least Common Multiples of 680

Related Least Common Multiples of 684

Frequently Asked Questions on LCM of 680 and 684

1. What is the LCM of 680 and 684?

Answer: LCM of 680 and 684 is 116280.

2. 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.

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 680 and 684?

Answer:

Least Common Multiple of 680 and 684 = 116280

Step 1: Find the prime factorization of 680

680 = 2 x 2 x 2 x 5 x 17

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 = 116280 = 2 x 2 x 2 x 3 x 3 x 5 x 17 x 19

Step 4: Therefore, the least common multiple of 680 and 684 is 116280.