Least Common Multiple of 504 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 504 and 512 the smallest integer that is 32256 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 512 is 32256.

LCM(504,512) = 32256

LCM of 504 and 512

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

LCM of:
and

Least Common Multiple of 504 and 512

LCM of 504 and 512 is 32256

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 512. First we will calculate the prime factors of 504 and 512.

Prime Factorization of 504


2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 504 are 2, 3,7. Prime factorization of 504 in exponential form is:

504 = 23×32×71

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 504 and 512.

LCM(504,512) = 29×32×71
LCM(504,512) = 32256

Factors of 504

List of positive integer factors of 504 that divides 504 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504

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 504 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 504 and 512, than apply into the LCM equation.

GCF(504,512) = 8
LCM(504,512) = ( 504 × 512) / 8
LCM(504,512) = 258048 / 8
LCM(504,512) = 32256

Properties of LCM 504 and 512

(i) The LCM of 512 and 504 is associative

LCM of 504 and 512 = LCM of 512 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 512

Frequently Asked Questions on LCM of 504 and 512

1. What is the LCM of 504 and 512?

Answer: LCM of 504 and 512 is 32256.

2. What are the Factors of 504?

Answer: Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. There are 24 integers that are factors of 504. The greatest factor of 504 is 504.

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 504 and 512?

Answer:

Least Common Multiple of 504 and 512 = 32256

Step 1: Find the prime factorization of 504

504 = 2 x 2 x 2 x 3 x 3 x 7

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 = 32256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 504 and 512 is 32256.