Least Common Multiple of 507 and 512

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 507 and 512 the smallest integer that is 259584 that is divisible by both numbers.

Least Common Multiple (LCM) of 507 and 512 is 259584.

LCM(507,512) = 259584

LCM of 507 and 512

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

LCM of:
and

Least Common Multiple of 507 and 512

LCM of 507 and 512 is 259584

Least common multiple can be found by multiplying the highest exponent prime factors of 507 and 512. First we will calculate the prime factors of 507 and 512.

Prime Factorization of 507


3 507
13 169
13 13
1

Prime factors of 507 are 3,13. Prime factorization of 507 in exponential form is:

507 = 31×132

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

Now multiplying the highest exponent prime factors to calculate the LCM of 507 and 512.

LCM(507,512) = 29×31×132
LCM(507,512) = 259584

Factors of 507

List of positive integer factors of 507 that divides 507 without a remainder.

1, 3, 13, 39, 169, 507

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

Least Common Multiple of 507 and 512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 507 and 512, than apply into the LCM equation.

GCF(507,512) = 1
LCM(507,512) = ( 507 × 512) / 1
LCM(507,512) = 259584 / 1
LCM(507,512) = 259584

Properties of LCM 507 and 512

(i) The LCM of 512 and 507 is associative

LCM of 507 and 512 = LCM of 512 and 507

Related Least Common Multiples of 507

Related Least Common Multiples of 512

Frequently Asked Questions on LCM of 507 and 512

1. What is the LCM of 507 and 512?

Answer: LCM of 507 and 512 is 259584.

2. What are the Factors of 507?

Answer: Factors of 507 are 1, 3, 13, 39, 169, 507. There are 6 integers that are factors of 507. The greatest factor of 507 is 507.

3. 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.

4. How to Find the LCM of 507 and 512?

Answer:

Least Common Multiple of 507 and 512 = 259584

Step 1: Find the prime factorization of 507

507 = 3 x 13 x 13

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 259584 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 13

Step 4: Therefore, the least common multiple of 507 and 512 is 259584.