Least Common Multiple of 60 and 66

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 60 and 66 the smallest integer that is 660 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 66 is 660.

LCM(60,66) = 660

LCM of 60 and 66

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

LCM of:
and

Least Common Multiple of 60 and 66

LCM of 60 and 66 is 660

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 66. First we will calculate the prime factors of 60 and 66.

Prime Factorization of 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

Prime Factorization of 66


2 66
3 33
11 11
1

Prime factors of 66 are 2, 3,11. Prime factorization of 66 in exponential form is:

66 = 21×31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 66.

LCM(60,66) = 22×31×51×111
LCM(60,66) = 660

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66

Least Common Multiple of 60 and 66 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 60 and 66, than apply into the LCM equation.

GCF(60,66) = 6
LCM(60,66) = ( 60 × 66) / 6
LCM(60,66) = 3960 / 6
LCM(60,66) = 660

Properties of LCM 60 and 66

(i) The LCM of 66 and 60 is associative

LCM of 60 and 66 = LCM of 66 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 66

Frequently Asked Questions on LCM of 60 and 66

1. What is the LCM of 60 and 66?

Answer: LCM of 60 and 66 is 660.

2. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

3. What are the Factors of 66?

Answer: Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. There are 8 integers that are factors of 66. The greatest factor of 66 is 66.

4. How to Find the LCM of 60 and 66?

Answer:

Least Common Multiple of 60 and 66 = 660

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 66

66 = 2 x 3 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 = 660 = 2 x 2 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 60 and 66 is 660.