Least Common Multiple of 512 and 514

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 512 and 514 the smallest integer that is 131584 that is divisible by both numbers.

Least Common Multiple (LCM) of 512 and 514 is 131584.

LCM(512,514) = 131584

LCM of 512 and 514

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

LCM of:
and

Least Common Multiple of 512 and 514

LCM of 512 and 514 is 131584

Least common multiple can be found by multiplying the highest exponent prime factors of 512 and 514. First we will calculate the prime factors of 512 and 514.

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

Prime Factorization of 514


2 514
257 257
1

Prime factors of 514 are 2,257. Prime factorization of 514 in exponential form is:

514 = 21×2571

Now multiplying the highest exponent prime factors to calculate the LCM of 512 and 514.

LCM(512,514) = 29×2571
LCM(512,514) = 131584

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

Factors of 514

List of positive integer factors of 514 that divides 514 without a remainder.

1, 2, 257, 514

Least Common Multiple of 512 and 514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 512 and 514, than apply into the LCM equation.

GCF(512,514) = 2
LCM(512,514) = ( 512 × 514) / 2
LCM(512,514) = 263168 / 2
LCM(512,514) = 131584

Properties of LCM 512 and 514

(i) The LCM of 514 and 512 is associative

LCM of 512 and 514 = LCM of 514 and 512

Related Least Common Multiples of 512

Related Least Common Multiples of 514

Frequently Asked Questions on LCM of 512 and 514

1. What is the LCM of 512 and 514?

Answer: LCM of 512 and 514 is 131584.

2. 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.

3. What are the Factors of 514?

Answer: Factors of 514 are 1, 2, 257, 514. There are 4 integers that are factors of 514. The greatest factor of 514 is 514.

4. How to Find the LCM of 512 and 514?

Answer:

Least Common Multiple of 512 and 514 = 131584

Step 1: 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 2: Find the prime factorization of 514

514 = 2 x 257

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

LCM = 131584 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 257

Step 4: Therefore, the least common multiple of 512 and 514 is 131584.