Least Common Multiple of 500 and 504

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 500 and 504 the smallest integer that is 63000 that is divisible by both numbers.

Least Common Multiple (LCM) of 500 and 504 is 63000.

LCM(500,504) = 63000

LCM of 500 and 504

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

LCM of:
and

Least Common Multiple of 500 and 504

LCM of 500 and 504 is 63000

Least common multiple can be found by multiplying the highest exponent prime factors of 500 and 504. First we will calculate the prime factors of 500 and 504.

Prime Factorization of 500


2 500
2 250
5 125
5 25
5 5
1

Prime factors of 500 are 2,5. Prime factorization of 500 in exponential form is:

500 = 22×53

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

Now multiplying the highest exponent prime factors to calculate the LCM of 500 and 504.

LCM(500,504) = 23×32×53×71
LCM(500,504) = 63000

Factors of 500

List of positive integer factors of 500 that divides 500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

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

Least Common Multiple of 500 and 504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 500 and 504, than apply into the LCM equation.

GCF(500,504) = 4
LCM(500,504) = ( 500 × 504) / 4
LCM(500,504) = 252000 / 4
LCM(500,504) = 63000

Properties of LCM 500 and 504

(i) The LCM of 504 and 500 is associative

LCM of 500 and 504 = LCM of 504 and 500

Related Least Common Multiples of 500

Related Least Common Multiples of 504

Frequently Asked Questions on LCM of 500 and 504

1. What is the LCM of 500 and 504?

Answer: LCM of 500 and 504 is 63000.

2. What are the Factors of 500?

Answer: Factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500. There are 12 integers that are factors of 500. The greatest factor of 500 is 500.

3. 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.

4. How to Find the LCM of 500 and 504?

Answer:

Least Common Multiple of 500 and 504 = 63000

Step 1: Find the prime factorization of 500

500 = 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 504

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

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

LCM = 63000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 500 and 504 is 63000.