Least Common Multiple of 688 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 688 and 690 the smallest integer that is 237360 that is divisible by both numbers.

Least Common Multiple (LCM) of 688 and 690 is 237360.

LCM(688,690) = 237360

LCM of 688 and 690

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

LCM of:
and

Least Common Multiple of 688 and 690

LCM of 688 and 690 is 237360

Least common multiple can be found by multiplying the highest exponent prime factors of 688 and 690. First we will calculate the prime factors of 688 and 690.

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

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 688 and 690.

LCM(688,690) = 24×31×51×231×431
LCM(688,690) = 237360

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

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 688 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 688 and 690, than apply into the LCM equation.

GCF(688,690) = 2
LCM(688,690) = ( 688 × 690) / 2
LCM(688,690) = 474720 / 2
LCM(688,690) = 237360

Properties of LCM 688 and 690

(i) The LCM of 690 and 688 is associative

LCM of 688 and 690 = LCM of 690 and 688

Related Least Common Multiples of 688

Related Least Common Multiples of 690

Frequently Asked Questions on LCM of 688 and 690

1. What is the LCM of 688 and 690?

Answer: LCM of 688 and 690 is 237360.

2. 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.

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 688 and 690?

Answer:

Least Common Multiple of 688 and 690 = 237360

Step 1: Find the prime factorization of 688

688 = 2 x 2 x 2 x 2 x 43

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 = 237360 = 2 x 2 x 2 x 2 x 3 x 5 x 23 x 43

Step 4: Therefore, the least common multiple of 688 and 690 is 237360.