Least Common Multiple of 256 and 264

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 256 and 264 the smallest integer that is 8448 that is divisible by both numbers.

Least Common Multiple (LCM) of 256 and 264 is 8448.

LCM(256,264) = 8448

LCM of 256 and 264

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

LCM of:
and

Least Common Multiple of 256 and 264

LCM of 256 and 264 is 8448

Least common multiple can be found by multiplying the highest exponent prime factors of 256 and 264. First we will calculate the prime factors of 256 and 264.

Prime Factorization of 256


2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 256 are 2. Prime factorization of 256 in exponential form is:

256 = 28

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

Now multiplying the highest exponent prime factors to calculate the LCM of 256 and 264.

LCM(256,264) = 28×31×111
LCM(256,264) = 8448

Factors of 256

List of positive integer factors of 256 that divides 256 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256

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

Least Common Multiple of 256 and 264 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 256 and 264, than apply into the LCM equation.

GCF(256,264) = 8
LCM(256,264) = ( 256 × 264) / 8
LCM(256,264) = 67584 / 8
LCM(256,264) = 8448

Properties of LCM 256 and 264

(i) The LCM of 264 and 256 is associative

LCM of 256 and 264 = LCM of 264 and 256

Related Least Common Multiples of 256

Related Least Common Multiples of 264

Frequently Asked Questions on LCM of 256 and 264

1. What is the LCM of 256 and 264?

Answer: LCM of 256 and 264 is 8448.

2. What are the Factors of 256?

Answer: Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256. There are 9 integers that are factors of 256. The greatest factor of 256 is 256.

3. 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.

4. How to Find the LCM of 256 and 264?

Answer:

Least Common Multiple of 256 and 264 = 8448

Step 1: Find the prime factorization of 256

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 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 = 8448 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11

Step 4: Therefore, the least common multiple of 256 and 264 is 8448.