Least Common Multiple of 684 and 690

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 684 and 690 the smallest integer that is 78660 that is divisible by both numbers.

Least Common Multiple (LCM) of 684 and 690 is 78660.

LCM(684,690) = 78660

LCM of 684 and 690

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

LCM of:
and

Least Common Multiple of 684 and 690

LCM of 684 and 690 is 78660

Least common multiple can be found by multiplying the highest exponent prime factors of 684 and 690. First we will calculate the prime factors of 684 and 690.

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

Prime Factorization of 690


2 690
3 345
5 115
23 23
1

Prime factors of 690 are 2, 3, 5,23. Prime factorization of 690 in exponential form is:

690 = 21×31×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 684 and 690.

LCM(684,690) = 22×32×51×191×231
LCM(684,690) = 78660

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

Factors of 690

List of positive integer factors of 690 that divides 690 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

Least Common Multiple of 684 and 690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 684 and 690, than apply into the LCM equation.

GCF(684,690) = 6
LCM(684,690) = ( 684 × 690) / 6
LCM(684,690) = 471960 / 6
LCM(684,690) = 78660

Properties of LCM 684 and 690

(i) The LCM of 690 and 684 is associative

LCM of 684 and 690 = LCM of 690 and 684

Related Least Common Multiples of 684

Related Least Common Multiples of 690

Frequently Asked Questions on LCM of 684 and 690

1. What is the LCM of 684 and 690?

Answer: LCM of 684 and 690 is 78660.

2. 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.

3. What are the Factors of 690?

Answer: Factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690. There are 16 integers that are factors of 690. The greatest factor of 690 is 690.

4. How to Find the LCM of 684 and 690?

Answer:

Least Common Multiple of 684 and 690 = 78660

Step 1: Find the prime factorization of 684

684 = 2 x 2 x 3 x 3 x 19

Step 2: Find the prime factorization of 690

690 = 2 x 3 x 5 x 23

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

LCM = 78660 = 2 x 2 x 3 x 3 x 5 x 19 x 23

Step 4: Therefore, the least common multiple of 684 and 690 is 78660.