Least Common Multiple of 675 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 675 and 680 the smallest integer that is 91800 that is divisible by both numbers.

Least Common Multiple (LCM) of 675 and 680 is 91800.

LCM(675,680) = 91800

LCM of 675 and 680

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

LCM of:
and

Least Common Multiple of 675 and 680

LCM of 675 and 680 is 91800

Least common multiple can be found by multiplying the highest exponent prime factors of 675 and 680. First we will calculate the prime factors of 675 and 680.

Prime Factorization of 675


3 675
3 225
3 75
5 25
5 5
1

Prime factors of 675 are 3,5. Prime factorization of 675 in exponential form is:

675 = 33×52

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 675 and 680.

LCM(675,680) = 23×33×52×171
LCM(675,680) = 91800

Factors of 675

List of positive integer factors of 675 that divides 675 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

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 675 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 675 and 680, than apply into the LCM equation.

GCF(675,680) = 5
LCM(675,680) = ( 675 × 680) / 5
LCM(675,680) = 459000 / 5
LCM(675,680) = 91800

Properties of LCM 675 and 680

(i) The LCM of 680 and 675 is associative

LCM of 675 and 680 = LCM of 680 and 675

Related Least Common Multiples of 675

Related Least Common Multiples of 680

Frequently Asked Questions on LCM of 675 and 680

1. What is the LCM of 675 and 680?

Answer: LCM of 675 and 680 is 91800.

2. What are the Factors of 675?

Answer: Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675. There are 12 integers that are factors of 675. The greatest factor of 675 is 675.

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 675 and 680?

Answer:

Least Common Multiple of 675 and 680 = 91800

Step 1: Find the prime factorization of 675

675 = 3 x 3 x 3 x 5 x 5

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 = 91800 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 17

Step 4: Therefore, the least common multiple of 675 and 680 is 91800.