Least Common Multiple of 684 and 689

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 689 the smallest integer that is 471276 that is divisible by both numbers.

Least Common Multiple (LCM) of 684 and 689 is 471276.

LCM(684,689) = 471276

LCM of 684 and 689

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

LCM of:
and

Least Common Multiple of 684 and 689

LCM of 684 and 689 is 471276

Least common multiple can be found by multiplying the highest exponent prime factors of 684 and 689. First we will calculate the prime factors of 684 and 689.

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 689


13 689
53 53
1

Prime factors of 689 are 13,53. Prime factorization of 689 in exponential form is:

689 = 131×531

Now multiplying the highest exponent prime factors to calculate the LCM of 684 and 689.

LCM(684,689) = 22×32×131×191×531
LCM(684,689) = 471276

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 689

List of positive integer factors of 689 that divides 689 without a remainder.

1, 13, 53, 689

Least Common Multiple of 684 and 689 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 689, than apply into the LCM equation.

GCF(684,689) = 1
LCM(684,689) = ( 684 × 689) / 1
LCM(684,689) = 471276 / 1
LCM(684,689) = 471276

Properties of LCM 684 and 689

(i) The LCM of 689 and 684 is associative

LCM of 684 and 689 = LCM of 689 and 684

Related Least Common Multiples of 684

Related Least Common Multiples of 689

Frequently Asked Questions on LCM of 684 and 689

1. What is the LCM of 684 and 689?

Answer: LCM of 684 and 689 is 471276.

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 689?

Answer: Factors of 689 are 1, 13, 53, 689. There are 4 integers that are factors of 689. The greatest factor of 689 is 689.

4. How to Find the LCM of 684 and 689?

Answer:

Least Common Multiple of 684 and 689 = 471276

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 689

689 = 13 x 53

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

LCM = 471276 = 2 x 2 x 3 x 3 x 13 x 19 x 53

Step 4: Therefore, the least common multiple of 684 and 689 is 471276.