Least Common Multiple of 60 and 65

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 65 the smallest integer that is 780 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 65 is 780.

LCM(60,65) = 780

LCM of 60 and 65

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

LCM of:
and

Least Common Multiple of 60 and 65

LCM of 60 and 65 is 780

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 65. First we will calculate the prime factors of 60 and 65.

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 65


5 65
13 13
1

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 65.

LCM(60,65) = 22×31×51×131
LCM(60,65) = 780

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 65

List of positive integer factors of 65 that divides 65 without a remainder.

1, 5, 13, 65

Least Common Multiple of 60 and 65 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 65, than apply into the LCM equation.

GCF(60,65) = 5
LCM(60,65) = ( 60 × 65) / 5
LCM(60,65) = 3900 / 5
LCM(60,65) = 780

Properties of LCM 60 and 65

(i) The LCM of 65 and 60 is associative

LCM of 60 and 65 = LCM of 65 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 65

Frequently Asked Questions on LCM of 60 and 65

1. What is the LCM of 60 and 65?

Answer: LCM of 60 and 65 is 780.

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 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

4. How to Find the LCM of 60 and 65?

Answer:

Least Common Multiple of 60 and 65 = 780

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 65

65 = 5 x 13

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

LCM = 780 = 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 60 and 65 is 780.