Least Common Multiple of 60 and 68

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 68 the smallest integer that is 1020 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 68 is 1020.

LCM(60,68) = 1020

LCM of 60 and 68

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

LCM of:
and

Least Common Multiple of 60 and 68

LCM of 60 and 68 is 1020

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 68. First we will calculate the prime factors of 60 and 68.

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 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 68.

LCM(60,68) = 22×31×51×171
LCM(60,68) = 1020

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 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34, 68

Least Common Multiple of 60 and 68 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 68, than apply into the LCM equation.

GCF(60,68) = 4
LCM(60,68) = ( 60 × 68) / 4
LCM(60,68) = 4080 / 4
LCM(60,68) = 1020

Properties of LCM 60 and 68

(i) The LCM of 68 and 60 is associative

LCM of 60 and 68 = LCM of 68 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 68

Frequently Asked Questions on LCM of 60 and 68

1. What is the LCM of 60 and 68?

Answer: LCM of 60 and 68 is 1020.

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 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the LCM of 60 and 68?

Answer:

Least Common Multiple of 60 and 68 = 1020

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 68

68 = 2 x 2 x 17

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

LCM = 1020 = 2 x 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 60 and 68 is 1020.