Least Common Multiple of 60 and 67

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 67 the smallest integer that is 4020 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 67 is 4020.

LCM(60,67) = 4020

LCM of 60 and 67

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

LCM of:
and

Least Common Multiple of 60 and 67

LCM of 60 and 67 is 4020

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 67. First we will calculate the prime factors of 60 and 67.

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 67


67 67
1

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 671

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 67.

LCM(60,67) = 22×31×51×671
LCM(60,67) = 4020

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 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

Least Common Multiple of 60 and 67 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 67, than apply into the LCM equation.

GCF(60,67) = 1
LCM(60,67) = ( 60 × 67) / 1
LCM(60,67) = 4020 / 1
LCM(60,67) = 4020

Properties of LCM 60 and 67

(i) The LCM of 67 and 60 is associative

LCM of 60 and 67 = LCM of 67 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 67

Frequently Asked Questions on LCM of 60 and 67

1. What is the LCM of 60 and 67?

Answer: LCM of 60 and 67 is 4020.

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 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

4. How to Find the LCM of 60 and 67?

Answer:

Least Common Multiple of 60 and 67 = 4020

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 4020 = 2 x 2 x 3 x 5 x 67

Step 4: Therefore, the least common multiple of 60 and 67 is 4020.