Least Common Multiple of 657 and 660

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 657 and 660 the smallest integer that is 144540 that is divisible by both numbers.

Least Common Multiple (LCM) of 657 and 660 is 144540.

LCM(657,660) = 144540

LCM of 657 and 660

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

LCM of:
and

Least Common Multiple of 657 and 660

LCM of 657 and 660 is 144540

Least common multiple can be found by multiplying the highest exponent prime factors of 657 and 660. First we will calculate the prime factors of 657 and 660.

Prime Factorization of 657


3 657
3 219
73 73
1

Prime factors of 657 are 3,73. Prime factorization of 657 in exponential form is:

657 = 32×731

Prime Factorization of 660


2 660
2 330
3 165
5 55
11 11
1

Prime factors of 660 are 2, 3, 5,11. Prime factorization of 660 in exponential form is:

660 = 22×31×51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 657 and 660.

LCM(657,660) = 22×32×51×111×731
LCM(657,660) = 144540

Factors of 657

List of positive integer factors of 657 that divides 657 without a remainder.

1, 3, 9, 73, 219, 657

Factors of 660

List of positive integer factors of 660 that divides 660 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660

Least Common Multiple of 657 and 660 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 657 and 660, than apply into the LCM equation.

GCF(657,660) = 3
LCM(657,660) = ( 657 × 660) / 3
LCM(657,660) = 433620 / 3
LCM(657,660) = 144540

Properties of LCM 657 and 660

(i) The LCM of 660 and 657 is associative

LCM of 657 and 660 = LCM of 660 and 657

Related Least Common Multiples of 657

Related Least Common Multiples of 660

Frequently Asked Questions on LCM of 657 and 660

1. What is the LCM of 657 and 660?

Answer: LCM of 657 and 660 is 144540.

2. What are the Factors of 657?

Answer: Factors of 657 are 1, 3, 9, 73, 219, 657. There are 6 integers that are factors of 657. The greatest factor of 657 is 657.

3. What are the Factors of 660?

Answer: Factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660. There are 24 integers that are factors of 660. The greatest factor of 660 is 660.

4. How to Find the LCM of 657 and 660?

Answer:

Least Common Multiple of 657 and 660 = 144540

Step 1: Find the prime factorization of 657

657 = 3 x 3 x 73

Step 2: Find the prime factorization of 660

660 = 2 x 2 x 3 x 5 x 11

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

LCM = 144540 = 2 x 2 x 3 x 3 x 5 x 11 x 73

Step 4: Therefore, the least common multiple of 657 and 660 is 144540.