Least Common Multiple of 506 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 506 and 514 the smallest integer that is 130042 that is divisible by both numbers.

Least Common Multiple (LCM) of 506 and 514 is 130042.

LCM(506,514) = 130042

LCM of 506 and 514

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

LCM of:
and

Least Common Multiple of 506 and 514

LCM of 506 and 514 is 130042

Least common multiple can be found by multiplying the highest exponent prime factors of 506 and 514. First we will calculate the prime factors of 506 and 514.

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 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 506 and 514.

LCM(506,514) = 21×111×231×2571
LCM(506,514) = 130042

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 514

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

1, 2, 257, 514

Least Common Multiple of 506 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 506 and 514, than apply into the LCM equation.

GCF(506,514) = 2
LCM(506,514) = ( 506 × 514) / 2
LCM(506,514) = 260084 / 2
LCM(506,514) = 130042

Properties of LCM 506 and 514

(i) The LCM of 514 and 506 is associative

LCM of 506 and 514 = LCM of 514 and 506

Related Least Common Multiples of 506

Related Least Common Multiples of 514

Frequently Asked Questions on LCM of 506 and 514

1. What is the LCM of 506 and 514?

Answer: LCM of 506 and 514 is 130042.

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 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 506 and 514?

Answer:

Least Common Multiple of 506 and 514 = 130042

Step 1: Find the prime factorization of 506

506 = 2 x 11 x 23

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 = 130042 = 2 x 11 x 23 x 257

Step 4: Therefore, the least common multiple of 506 and 514 is 130042.