Least Common Multiple of 504 and 507

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 507 the smallest integer that is 85176 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 507 is 85176.

LCM(504,507) = 85176

LCM of 504 and 507

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

LCM of:
and

Least Common Multiple of 504 and 507

LCM of 504 and 507 is 85176

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 507. First we will calculate the prime factors of 504 and 507.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 507.

LCM(504,507) = 23×32×71×132
LCM(504,507) = 85176

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 507

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

1, 3, 13, 39, 169, 507

Least Common Multiple of 504 and 507 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 507, than apply into the LCM equation.

GCF(504,507) = 3
LCM(504,507) = ( 504 × 507) / 3
LCM(504,507) = 255528 / 3
LCM(504,507) = 85176

Properties of LCM 504 and 507

(i) The LCM of 507 and 504 is associative

LCM of 504 and 507 = LCM of 507 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 507

Frequently Asked Questions on LCM of 504 and 507

1. What is the LCM of 504 and 507?

Answer: LCM of 504 and 507 is 85176.

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 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.

4. How to Find the LCM of 504 and 507?

Answer:

Least Common Multiple of 504 and 507 = 85176

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 507

507 = 3 x 13 x 13

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

LCM = 85176 = 2 x 2 x 2 x 3 x 3 x 7 x 13 x 13

Step 4: Therefore, the least common multiple of 504 and 507 is 85176.