Least Common Multiple of 264 and 270

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 264 and 270 the smallest integer that is 11880 that is divisible by both numbers.

Least Common Multiple (LCM) of 264 and 270 is 11880.

LCM(264,270) = 11880

LCM of 264 and 270

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

LCM of:
and

Least Common Multiple of 264 and 270

LCM of 264 and 270 is 11880

Least common multiple can be found by multiplying the highest exponent prime factors of 264 and 270. First we will calculate the prime factors of 264 and 270.

Prime Factorization of 264


2 264
2 132
2 66
3 33
11 11
1

Prime factors of 264 are 2, 3,11. Prime factorization of 264 in exponential form is:

264 = 23×31×111

Prime Factorization of 270


2 270
3 135
3 45
3 15
5 5
1

Prime factors of 270 are 2, 3,5. Prime factorization of 270 in exponential form is:

270 = 21×33×51

Now multiplying the highest exponent prime factors to calculate the LCM of 264 and 270.

LCM(264,270) = 23×33×51×111
LCM(264,270) = 11880

Factors of 264

List of positive integer factors of 264 that divides 264 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264

Factors of 270

List of positive integer factors of 270 that divides 270 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

Least Common Multiple of 264 and 270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 264 and 270, than apply into the LCM equation.

GCF(264,270) = 6
LCM(264,270) = ( 264 × 270) / 6
LCM(264,270) = 71280 / 6
LCM(264,270) = 11880

Properties of LCM 264 and 270

(i) The LCM of 270 and 264 is associative

LCM of 264 and 270 = LCM of 270 and 264

Related Least Common Multiples of 264

Related Least Common Multiples of 270

Frequently Asked Questions on LCM of 264 and 270

1. What is the LCM of 264 and 270?

Answer: LCM of 264 and 270 is 11880.

2. What are the Factors of 264?

Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.

3. What are the Factors of 270?

Answer: Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270. There are 16 integers that are factors of 270. The greatest factor of 270 is 270.

4. How to Find the LCM of 264 and 270?

Answer:

Least Common Multiple of 264 and 270 = 11880

Step 1: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 270

270 = 2 x 3 x 3 x 3 x 5

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

LCM = 11880 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 264 and 270 is 11880.