Least Common Multiple of 504 and 508

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 508 the smallest integer that is 64008 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 508 is 64008.

LCM(504,508) = 64008

LCM of 504 and 508

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

LCM of:
and

Least Common Multiple of 504 and 508

LCM of 504 and 508 is 64008

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 508. First we will calculate the prime factors of 504 and 508.

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 508


2 508
2 254
127 127
1

Prime factors of 508 are 2,127. Prime factorization of 508 in exponential form is:

508 = 22×1271

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 508.

LCM(504,508) = 23×32×71×1271
LCM(504,508) = 64008

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 508

List of positive integer factors of 508 that divides 508 without a remainder.

1, 2, 4, 127, 254, 508

Least Common Multiple of 504 and 508 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 508, than apply into the LCM equation.

GCF(504,508) = 4
LCM(504,508) = ( 504 × 508) / 4
LCM(504,508) = 256032 / 4
LCM(504,508) = 64008

Properties of LCM 504 and 508

(i) The LCM of 508 and 504 is associative

LCM of 504 and 508 = LCM of 508 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 508

Frequently Asked Questions on LCM of 504 and 508

1. What is the LCM of 504 and 508?

Answer: LCM of 504 and 508 is 64008.

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 508?

Answer: Factors of 508 are 1, 2, 4, 127, 254, 508. There are 6 integers that are factors of 508. The greatest factor of 508 is 508.

4. How to Find the LCM of 504 and 508?

Answer:

Least Common Multiple of 504 and 508 = 64008

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 508

508 = 2 x 2 x 127

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

LCM = 64008 = 2 x 2 x 2 x 3 x 3 x 7 x 127

Step 4: Therefore, the least common multiple of 504 and 508 is 64008.