Least Common Multiple of 60 and 77

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 77 the smallest integer that is 4620 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 77 is 4620.

LCM(60,77) = 4620

LCM of 60 and 77

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

LCM of:
and

Least Common Multiple of 60 and 77

LCM of 60 and 77 is 4620

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 77. First we will calculate the prime factors of 60 and 77.

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 77


7 77
11 11
1

Prime factors of 77 are 7,11. Prime factorization of 77 in exponential form is:

77 = 71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 77.

LCM(60,77) = 22×31×51×71×111
LCM(60,77) = 4620

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 77

List of positive integer factors of 77 that divides 77 without a remainder.

1, 7, 11, 77

Least Common Multiple of 60 and 77 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 77, than apply into the LCM equation.

GCF(60,77) = 1
LCM(60,77) = ( 60 × 77) / 1
LCM(60,77) = 4620 / 1
LCM(60,77) = 4620

Properties of LCM 60 and 77

(i) The LCM of 77 and 60 is associative

LCM of 60 and 77 = LCM of 77 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 77

Frequently Asked Questions on LCM of 60 and 77

1. What is the LCM of 60 and 77?

Answer: LCM of 60 and 77 is 4620.

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 77?

Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.

4. How to Find the LCM of 60 and 77?

Answer:

Least Common Multiple of 60 and 77 = 4620

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 77

77 = 7 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 = 4620 = 2 x 2 x 3 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 60 and 77 is 4620.