Least Common Multiple of 514 and 520

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 514 and 520 the smallest integer that is 133640 that is divisible by both numbers.

Least Common Multiple (LCM) of 514 and 520 is 133640.

LCM(514,520) = 133640

LCM of 514 and 520

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

LCM of:
and

Least Common Multiple of 514 and 520

LCM of 514 and 520 is 133640

Least common multiple can be found by multiplying the highest exponent prime factors of 514 and 520. First we will calculate the prime factors of 514 and 520.

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

Prime Factorization of 520


2 520
2 260
2 130
5 65
13 13
1

Prime factors of 520 are 2, 5,13. Prime factorization of 520 in exponential form is:

520 = 23×51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 514 and 520.

LCM(514,520) = 23×51×131×2571
LCM(514,520) = 133640

Factors of 514

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

1, 2, 257, 514

Factors of 520

List of positive integer factors of 520 that divides 520 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

Least Common Multiple of 514 and 520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 514 and 520, than apply into the LCM equation.

GCF(514,520) = 2
LCM(514,520) = ( 514 × 520) / 2
LCM(514,520) = 267280 / 2
LCM(514,520) = 133640

Properties of LCM 514 and 520

(i) The LCM of 520 and 514 is associative

LCM of 514 and 520 = LCM of 520 and 514

Related Least Common Multiples of 514

Related Least Common Multiples of 520

Frequently Asked Questions on LCM of 514 and 520

1. What is the LCM of 514 and 520?

Answer: LCM of 514 and 520 is 133640.

2. 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.

3. What are the Factors of 520?

Answer: Factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520. There are 16 integers that are factors of 520. The greatest factor of 520 is 520.

4. How to Find the LCM of 514 and 520?

Answer:

Least Common Multiple of 514 and 520 = 133640

Step 1: Find the prime factorization of 514

514 = 2 x 257

Step 2: Find the prime factorization of 520

520 = 2 x 2 x 2 x 5 x 13

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

LCM = 133640 = 2 x 2 x 2 x 5 x 13 x 257

Step 4: Therefore, the least common multiple of 514 and 520 is 133640.