Least Common Multiple of 255 and 256

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 255 and 256 the smallest integer that is 65280 that is divisible by both numbers.

Least Common Multiple (LCM) of 255 and 256 is 65280.

LCM(255,256) = 65280

LCM of 255 and 256

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

LCM of:
and

Least Common Multiple of 255 and 256

LCM of 255 and 256 is 65280

Least common multiple can be found by multiplying the highest exponent prime factors of 255 and 256. First we will calculate the prime factors of 255 and 256.

Prime Factorization of 255


3 255
5 85
17 17
1

Prime factors of 255 are 3, 5,17. Prime factorization of 255 in exponential form is:

255 = 31×51×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 255 and 256.

LCM(255,256) = 28×31×51×171
LCM(255,256) = 65280

Factors of 255

List of positive integer factors of 255 that divides 255 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255

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

Least Common Multiple of 255 and 256 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 255 and 256, than apply into the LCM equation.

GCF(255,256) = 1
LCM(255,256) = ( 255 × 256) / 1
LCM(255,256) = 65280 / 1
LCM(255,256) = 65280

Properties of LCM 255 and 256

(i) The LCM of 256 and 255 is associative

LCM of 255 and 256 = LCM of 256 and 255

Related Least Common Multiples of 255

Related Least Common Multiples of 256

Frequently Asked Questions on LCM of 255 and 256

1. What is the LCM of 255 and 256?

Answer: LCM of 255 and 256 is 65280.

2. What are the Factors of 255?

Answer: Factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255. There are 8 integers that are factors of 255. The greatest factor of 255 is 255.

3. 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.

4. How to Find the LCM of 255 and 256?

Answer:

Least Common Multiple of 255 and 256 = 65280

Step 1: Find the prime factorization of 255

255 = 3 x 5 x 17

Step 2: Find the prime factorization of 256

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

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

LCM = 65280 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 255 and 256 is 65280.