Least Common Multiple of 60 and 69

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 69 the smallest integer that is 1380 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 69 is 1380.

LCM(60,69) = 1380

LCM of 60 and 69

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

LCM of:
and

Least Common Multiple of 60 and 69

LCM of 60 and 69 is 1380

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 69. First we will calculate the prime factors of 60 and 69.

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 69


3 69
23 23
1

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 31×231

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 69.

LCM(60,69) = 22×31×51×231
LCM(60,69) = 1380

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 69

List of positive integer factors of 69 that divides 69 without a remainder.

1, 3, 23, 69

Least Common Multiple of 60 and 69 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 69, than apply into the LCM equation.

GCF(60,69) = 3
LCM(60,69) = ( 60 × 69) / 3
LCM(60,69) = 4140 / 3
LCM(60,69) = 1380

Properties of LCM 60 and 69

(i) The LCM of 69 and 60 is associative

LCM of 60 and 69 = LCM of 69 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 69

Frequently Asked Questions on LCM of 60 and 69

1. What is the LCM of 60 and 69?

Answer: LCM of 60 and 69 is 1380.

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 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the LCM of 60 and 69?

Answer:

Least Common Multiple of 60 and 69 = 1380

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 69

69 = 3 x 23

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

LCM = 1380 = 2 x 2 x 3 x 5 x 23

Step 4: Therefore, the least common multiple of 60 and 69 is 1380.