Least Common Multiple of 504 and 506

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 506 the smallest integer that is 127512 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 506 is 127512.

LCM(504,506) = 127512

LCM of 504 and 506

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

LCM of:
and

Least Common Multiple of 504 and 506

LCM of 504 and 506 is 127512

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 506. First we will calculate the prime factors of 504 and 506.

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 506


2 506
11 253
23 23
1

Prime factors of 506 are 2, 11,23. Prime factorization of 506 in exponential form is:

506 = 21×111×231

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 506.

LCM(504,506) = 23×32×71×111×231
LCM(504,506) = 127512

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 506

List of positive integer factors of 506 that divides 506 without a remainder.

1, 2, 11, 22, 23, 46, 253, 506

Least Common Multiple of 504 and 506 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 506, than apply into the LCM equation.

GCF(504,506) = 2
LCM(504,506) = ( 504 × 506) / 2
LCM(504,506) = 255024 / 2
LCM(504,506) = 127512

Properties of LCM 504 and 506

(i) The LCM of 506 and 504 is associative

LCM of 504 and 506 = LCM of 506 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 506

Frequently Asked Questions on LCM of 504 and 506

1. What is the LCM of 504 and 506?

Answer: LCM of 504 and 506 is 127512.

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 506?

Answer: Factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506. There are 8 integers that are factors of 506. The greatest factor of 506 is 506.

4. How to Find the LCM of 504 and 506?

Answer:

Least Common Multiple of 504 and 506 = 127512

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 506

506 = 2 x 11 x 23

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

LCM = 127512 = 2 x 2 x 2 x 3 x 3 x 7 x 11 x 23

Step 4: Therefore, the least common multiple of 504 and 506 is 127512.