Least Common Multiple of 264 and 272

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 272 the smallest integer that is 8976 that is divisible by both numbers.

Least Common Multiple (LCM) of 264 and 272 is 8976.

LCM(264,272) = 8976

LCM of 264 and 272

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

LCM of:
and

Least Common Multiple of 264 and 272

LCM of 264 and 272 is 8976

Least common multiple can be found by multiplying the highest exponent prime factors of 264 and 272. First we will calculate the prime factors of 264 and 272.

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 272


2 272
2 136
2 68
2 34
17 17
1

Prime factors of 272 are 2,17. Prime factorization of 272 in exponential form is:

272 = 24×171

Now multiplying the highest exponent prime factors to calculate the LCM of 264 and 272.

LCM(264,272) = 24×31×111×171
LCM(264,272) = 8976

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 272

List of positive integer factors of 272 that divides 272 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 272

Least Common Multiple of 264 and 272 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 272, than apply into the LCM equation.

GCF(264,272) = 8
LCM(264,272) = ( 264 × 272) / 8
LCM(264,272) = 71808 / 8
LCM(264,272) = 8976

Properties of LCM 264 and 272

(i) The LCM of 272 and 264 is associative

LCM of 264 and 272 = LCM of 272 and 264

Related Least Common Multiples of 264

Related Least Common Multiples of 272

Frequently Asked Questions on LCM of 264 and 272

1. What is the LCM of 264 and 272?

Answer: LCM of 264 and 272 is 8976.

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 272?

Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.

4. How to Find the LCM of 264 and 272?

Answer:

Least Common Multiple of 264 and 272 = 8976

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 272

272 = 2 x 2 x 2 x 2 x 17

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

LCM = 8976 = 2 x 2 x 2 x 2 x 3 x 11 x 17

Step 4: Therefore, the least common multiple of 264 and 272 is 8976.