Least Common Multiple of 506 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 506 and 510 the smallest integer that is 129030 that is divisible by both numbers.

Least Common Multiple (LCM) of 506 and 510 is 129030.

LCM(506,510) = 129030

LCM of 506 and 510

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

LCM of:
and

Least Common Multiple of 506 and 510

LCM of 506 and 510 is 129030

Least common multiple can be found by multiplying the highest exponent prime factors of 506 and 510. First we will calculate the prime factors of 506 and 510.

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

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 506 and 510.

LCM(506,510) = 21×31×51×111×171×231
LCM(506,510) = 129030

Factors of 506

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

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

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 506 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 506 and 510, than apply into the LCM equation.

GCF(506,510) = 2
LCM(506,510) = ( 506 × 510) / 2
LCM(506,510) = 258060 / 2
LCM(506,510) = 129030

Properties of LCM 506 and 510

(i) The LCM of 510 and 506 is associative

LCM of 506 and 510 = LCM of 510 and 506

Related Least Common Multiples of 506

Related Least Common Multiples of 510

Frequently Asked Questions on LCM of 506 and 510

1. What is the LCM of 506 and 510?

Answer: LCM of 506 and 510 is 129030.

2. 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.

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 506 and 510?

Answer:

Least Common Multiple of 506 and 510 = 129030

Step 1: Find the prime factorization of 506

506 = 2 x 11 x 23

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 = 129030 = 2 x 3 x 5 x 11 x 17 x 23

Step 4: Therefore, the least common multiple of 506 and 510 is 129030.