Least Common Multiple of 256 and 262

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 262 the smallest integer that is 33536 that is divisible by both numbers.

Least Common Multiple (LCM) of 256 and 262 is 33536.

LCM(256,262) = 33536

LCM of 256 and 262

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

LCM of:
and

Least Common Multiple of 256 and 262

LCM of 256 and 262 is 33536

Least common multiple can be found by multiplying the highest exponent prime factors of 256 and 262. First we will calculate the prime factors of 256 and 262.

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 262


2 262
131 131
1

Prime factors of 262 are 2,131. Prime factorization of 262 in exponential form is:

262 = 21×1311

Now multiplying the highest exponent prime factors to calculate the LCM of 256 and 262.

LCM(256,262) = 28×1311
LCM(256,262) = 33536

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 262

List of positive integer factors of 262 that divides 262 without a remainder.

1, 2, 131, 262

Least Common Multiple of 256 and 262 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 262, than apply into the LCM equation.

GCF(256,262) = 2
LCM(256,262) = ( 256 × 262) / 2
LCM(256,262) = 67072 / 2
LCM(256,262) = 33536

Properties of LCM 256 and 262

(i) The LCM of 262 and 256 is associative

LCM of 256 and 262 = LCM of 262 and 256

Related Least Common Multiples of 256

Related Least Common Multiples of 262

Frequently Asked Questions on LCM of 256 and 262

1. What is the LCM of 256 and 262?

Answer: LCM of 256 and 262 is 33536.

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 262?

Answer: Factors of 262 are 1, 2, 131, 262. There are 4 integers that are factors of 262. The greatest factor of 262 is 262.

4. How to Find the LCM of 256 and 262?

Answer:

Least Common Multiple of 256 and 262 = 33536

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 262

262 = 2 x 131

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

LCM = 33536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 131

Step 4: Therefore, the least common multiple of 256 and 262 is 33536.