Least Common Multiple of 504 and 509

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 509 the smallest integer that is 256536 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 509 is 256536.

LCM(504,509) = 256536

LCM of 504 and 509

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

LCM of:
and

Least Common Multiple of 504 and 509

LCM of 504 and 509 is 256536

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 509. First we will calculate the prime factors of 504 and 509.

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 509


509 509
1

Prime factors of 509 are 509. Prime factorization of 509 in exponential form is:

509 = 5091

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 509.

LCM(504,509) = 23×32×71×5091
LCM(504,509) = 256536

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 509

List of positive integer factors of 509 that divides 509 without a remainder.

1, 509

Least Common Multiple of 504 and 509 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 509, than apply into the LCM equation.

GCF(504,509) = 1
LCM(504,509) = ( 504 × 509) / 1
LCM(504,509) = 256536 / 1
LCM(504,509) = 256536

Properties of LCM 504 and 509

(i) The LCM of 509 and 504 is associative

LCM of 504 and 509 = LCM of 509 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 509

Frequently Asked Questions on LCM of 504 and 509

1. What is the LCM of 504 and 509?

Answer: LCM of 504 and 509 is 256536.

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 509?

Answer: Factors of 509 are 1, 509. There are 2 integers that are factors of 509. The greatest factor of 509 is 509.

4. How to Find the LCM of 504 and 509?

Answer:

Least Common Multiple of 504 and 509 = 256536

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 509

509 = 509

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

LCM = 256536 = 2 x 2 x 2 x 3 x 3 x 7 x 509

Step 4: Therefore, the least common multiple of 504 and 509 is 256536.