Least Common Multiple of 513 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 513 and 514 the smallest integer that is 263682 that is divisible by both numbers.

Least Common Multiple (LCM) of 513 and 514 is 263682.

LCM(513,514) = 263682

LCM of 513 and 514

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

LCM of:
and

Least Common Multiple of 513 and 514

LCM of 513 and 514 is 263682

Least common multiple can be found by multiplying the highest exponent prime factors of 513 and 514. First we will calculate the prime factors of 513 and 514.

Prime Factorization of 513


3 513
3 171
3 57
19 19
1

Prime factors of 513 are 3,19. Prime factorization of 513 in exponential form is:

513 = 33×191

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 513 and 514.

LCM(513,514) = 21×33×191×2571
LCM(513,514) = 263682

Factors of 513

List of positive integer factors of 513 that divides 513 without a remainder.

1, 3, 9, 19, 27, 57, 171, 513

Factors of 514

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

1, 2, 257, 514

Least Common Multiple of 513 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 513 and 514, than apply into the LCM equation.

GCF(513,514) = 1
LCM(513,514) = ( 513 × 514) / 1
LCM(513,514) = 263682 / 1
LCM(513,514) = 263682

Properties of LCM 513 and 514

(i) The LCM of 514 and 513 is associative

LCM of 513 and 514 = LCM of 514 and 513

Related Least Common Multiples of 513

Related Least Common Multiples of 514

Frequently Asked Questions on LCM of 513 and 514

1. What is the LCM of 513 and 514?

Answer: LCM of 513 and 514 is 263682.

2. What are the Factors of 513?

Answer: Factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513. There are 8 integers that are factors of 513. The greatest factor of 513 is 513.

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 513 and 514?

Answer:

Least Common Multiple of 513 and 514 = 263682

Step 1: Find the prime factorization of 513

513 = 3 x 3 x 3 x 19

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 = 263682 = 2 x 3 x 3 x 3 x 19 x 257

Step 4: Therefore, the least common multiple of 513 and 514 is 263682.