Least Common Multiple of 504 and 510

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 510 the smallest integer that is 42840 that is divisible by both numbers.

Least Common Multiple (LCM) of 504 and 510 is 42840.

LCM(504,510) = 42840

LCM of 504 and 510

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

LCM of:
and

Least Common Multiple of 504 and 510

LCM of 504 and 510 is 42840

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 510. First we will calculate the prime factors of 504 and 510.

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 510


2 510
3 255
5 85
17 17
1

Prime factors of 510 are 2, 3, 5,17. Prime factorization of 510 in exponential form is:

510 = 21×31×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 510.

LCM(504,510) = 23×32×51×71×171
LCM(504,510) = 42840

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 510

List of positive integer factors of 510 that divides 510 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

Least Common Multiple of 504 and 510 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 510, than apply into the LCM equation.

GCF(504,510) = 6
LCM(504,510) = ( 504 × 510) / 6
LCM(504,510) = 257040 / 6
LCM(504,510) = 42840

Properties of LCM 504 and 510

(i) The LCM of 510 and 504 is associative

LCM of 504 and 510 = LCM of 510 and 504

Related Least Common Multiples of 504

Related Least Common Multiples of 510

Frequently Asked Questions on LCM of 504 and 510

1. What is the LCM of 504 and 510?

Answer: LCM of 504 and 510 is 42840.

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 510?

Answer: Factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. There are 16 integers that are factors of 510. The greatest factor of 510 is 510.

4. How to Find the LCM of 504 and 510?

Answer:

Least Common Multiple of 504 and 510 = 42840

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 510

510 = 2 x 3 x 5 x 17

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

LCM = 42840 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 504 and 510 is 42840.