Least Common Multiple of 512 and 513

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 512 and 513 the smallest integer that is 262656 that is divisible by both numbers.

Least Common Multiple (LCM) of 512 and 513 is 262656.

LCM(512,513) = 262656

LCM of 512 and 513

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

LCM of:
and

Least Common Multiple of 512 and 513

LCM of 512 and 513 is 262656

Least common multiple can be found by multiplying the highest exponent prime factors of 512 and 513. First we will calculate the prime factors of 512 and 513.

Prime Factorization of 512


2 512
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 512 are 2. Prime factorization of 512 in exponential form is:

512 = 29

Prime Factorization of 513


3 513
3 171
3 57
19 19
1

Prime factors of 513 are 3,19. Prime factorization of 513 in exponential form is:

513 = 33×191

Now multiplying the highest exponent prime factors to calculate the LCM of 512 and 513.

LCM(512,513) = 29×33×191
LCM(512,513) = 262656

Factors of 512

List of positive integer factors of 512 that divides 512 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Factors of 513

List of positive integer factors of 513 that divides 513 without a remainder.

1, 3, 9, 19, 27, 57, 171, 513

Least Common Multiple of 512 and 513 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 512 and 513, than apply into the LCM equation.

GCF(512,513) = 1
LCM(512,513) = ( 512 × 513) / 1
LCM(512,513) = 262656 / 1
LCM(512,513) = 262656

Properties of LCM 512 and 513

(i) The LCM of 513 and 512 is associative

LCM of 512 and 513 = LCM of 513 and 512

Related Least Common Multiples of 512

Related Least Common Multiples of 513

Frequently Asked Questions on LCM of 512 and 513

1. What is the LCM of 512 and 513?

Answer: LCM of 512 and 513 is 262656.

2. What are the Factors of 512?

Answer: Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. There are 10 integers that are factors of 512. The greatest factor of 512 is 512.

3. What are the Factors of 513?

Answer: Factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513. There are 8 integers that are factors of 513. The greatest factor of 513 is 513.

4. How to Find the LCM of 512 and 513?

Answer:

Least Common Multiple of 512 and 513 = 262656

Step 1: Find the prime factorization of 512

512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

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

LCM = 262656 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19

Step 4: Therefore, the least common multiple of 512 and 513 is 262656.