Least Common Multiple of 256 and 257

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 257 the smallest integer that is 65792 that is divisible by both numbers.

Least Common Multiple (LCM) of 256 and 257 is 65792.

LCM(256,257) = 65792

LCM of 256 and 257

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

LCM of:
and

Least Common Multiple of 256 and 257

LCM of 256 and 257 is 65792

Least common multiple can be found by multiplying the highest exponent prime factors of 256 and 257. First we will calculate the prime factors of 256 and 257.

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 257


257 257
1

Prime factors of 257 are 257. Prime factorization of 257 in exponential form is:

257 = 2571

Now multiplying the highest exponent prime factors to calculate the LCM of 256 and 257.

LCM(256,257) = 28×2571
LCM(256,257) = 65792

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 257

List of positive integer factors of 257 that divides 257 without a remainder.

1, 257

Least Common Multiple of 256 and 257 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 257, than apply into the LCM equation.

GCF(256,257) = 1
LCM(256,257) = ( 256 × 257) / 1
LCM(256,257) = 65792 / 1
LCM(256,257) = 65792

Properties of LCM 256 and 257

(i) The LCM of 257 and 256 is associative

LCM of 256 and 257 = LCM of 257 and 256

Related Least Common Multiples of 256

Related Least Common Multiples of 257

Frequently Asked Questions on LCM of 256 and 257

1. What is the LCM of 256 and 257?

Answer: LCM of 256 and 257 is 65792.

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 257?

Answer: Factors of 257 are 1, 257. There are 2 integers that are factors of 257. The greatest factor of 257 is 257.

4. How to Find the LCM of 256 and 257?

Answer:

Least Common Multiple of 256 and 257 = 65792

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 257

257 = 257

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

LCM = 65792 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 257

Step 4: Therefore, the least common multiple of 256 and 257 is 65792.