Least Common Multiple of 510 and 512

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 510 and 512 the smallest integer that is 130560 that is divisible by both numbers.

Least Common Multiple (LCM) of 510 and 512 is 130560.

LCM(510,512) = 130560

LCM of 510 and 512

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

LCM of:
and

Least Common Multiple of 510 and 512

LCM of 510 and 512 is 130560

Least common multiple can be found by multiplying the highest exponent prime factors of 510 and 512. First we will calculate the prime factors of 510 and 512.

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

Prime Factorization of 512


2 512
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 512 are 2. Prime factorization of 512 in exponential form is:

512 = 29

Now multiplying the highest exponent prime factors to calculate the LCM of 510 and 512.

LCM(510,512) = 29×31×51×171
LCM(510,512) = 130560

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

Factors of 512

List of positive integer factors of 512 that divides 512 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Least Common Multiple of 510 and 512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 510 and 512, than apply into the LCM equation.

GCF(510,512) = 2
LCM(510,512) = ( 510 × 512) / 2
LCM(510,512) = 261120 / 2
LCM(510,512) = 130560

Properties of LCM 510 and 512

(i) The LCM of 512 and 510 is associative

LCM of 510 and 512 = LCM of 512 and 510

Related Least Common Multiples of 510

Related Least Common Multiples of 512

Frequently Asked Questions on LCM of 510 and 512

1. What is the LCM of 510 and 512?

Answer: LCM of 510 and 512 is 130560.

2. 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.

3. What are the Factors of 512?

Answer: Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. There are 10 integers that are factors of 512. The greatest factor of 512 is 512.

4. How to Find the LCM of 510 and 512?

Answer:

Least Common Multiple of 510 and 512 = 130560

Step 1: Find the prime factorization of 510

510 = 2 x 3 x 5 x 17

Step 2: Find the prime factorization of 512

512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

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

LCM = 130560 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 510 and 512 is 130560.