Least Common Multiple of 654 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 654 and 660 the smallest integer that is 71940 that is divisible by both numbers.

Least Common Multiple (LCM) of 654 and 660 is 71940.

LCM(654,660) = 71940

LCM of 654 and 660

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

LCM of:
and

Least Common Multiple of 654 and 660

LCM of 654 and 660 is 71940

Least common multiple can be found by multiplying the highest exponent prime factors of 654 and 660. First we will calculate the prime factors of 654 and 660.

Prime Factorization of 654


2 654
3 327
109 109
1

Prime factors of 654 are 2, 3,109. Prime factorization of 654 in exponential form is:

654 = 21×31×1091

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 654 and 660.

LCM(654,660) = 22×31×51×111×1091
LCM(654,660) = 71940

Factors of 654

List of positive integer factors of 654 that divides 654 without a remainder.

1, 2, 3, 6, 109, 218, 327, 654

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 654 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 654 and 660, than apply into the LCM equation.

GCF(654,660) = 6
LCM(654,660) = ( 654 × 660) / 6
LCM(654,660) = 431640 / 6
LCM(654,660) = 71940

Properties of LCM 654 and 660

(i) The LCM of 660 and 654 is associative

LCM of 654 and 660 = LCM of 660 and 654

Related Least Common Multiples of 654

Related Least Common Multiples of 660

Frequently Asked Questions on LCM of 654 and 660

1. What is the LCM of 654 and 660?

Answer: LCM of 654 and 660 is 71940.

2. What are the Factors of 654?

Answer: Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654. There are 8 integers that are factors of 654. The greatest factor of 654 is 654.

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 654 and 660?

Answer:

Least Common Multiple of 654 and 660 = 71940

Step 1: Find the prime factorization of 654

654 = 2 x 3 x 109

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 = 71940 = 2 x 2 x 3 x 5 x 11 x 109

Step 4: Therefore, the least common multiple of 654 and 660 is 71940.