Least Common Multiple of 684 and 688

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 688 the smallest integer that is 117648 that is divisible by both numbers.

Least Common Multiple (LCM) of 684 and 688 is 117648.

LCM(684,688) = 117648

LCM of 684 and 688

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

LCM of:
and

Least Common Multiple of 684 and 688

LCM of 684 and 688 is 117648

Least common multiple can be found by multiplying the highest exponent prime factors of 684 and 688. First we will calculate the prime factors of 684 and 688.

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 688


2 688
2 344
2 172
2 86
43 43
1

Prime factors of 688 are 2,43. Prime factorization of 688 in exponential form is:

688 = 24×431

Now multiplying the highest exponent prime factors to calculate the LCM of 684 and 688.

LCM(684,688) = 24×32×191×431
LCM(684,688) = 117648

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 688

List of positive integer factors of 688 that divides 688 without a remainder.

1, 2, 4, 8, 16, 43, 86, 172, 344, 688

Least Common Multiple of 684 and 688 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 688, than apply into the LCM equation.

GCF(684,688) = 4
LCM(684,688) = ( 684 × 688) / 4
LCM(684,688) = 470592 / 4
LCM(684,688) = 117648

Properties of LCM 684 and 688

(i) The LCM of 688 and 684 is associative

LCM of 684 and 688 = LCM of 688 and 684

Related Least Common Multiples of 684

Related Least Common Multiples of 688

Frequently Asked Questions on LCM of 684 and 688

1. What is the LCM of 684 and 688?

Answer: LCM of 684 and 688 is 117648.

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 688?

Answer: Factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688. There are 10 integers that are factors of 688. The greatest factor of 688 is 688.

4. How to Find the LCM of 684 and 688?

Answer:

Least Common Multiple of 684 and 688 = 117648

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 688

688 = 2 x 2 x 2 x 2 x 43

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

LCM = 117648 = 2 x 2 x 2 x 2 x 3 x 3 x 19 x 43

Step 4: Therefore, the least common multiple of 684 and 688 is 117648.