Least Common Multiple of 514 and 522

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 522 the smallest integer that is 134154 that is divisible by both numbers.

Least Common Multiple (LCM) of 514 and 522 is 134154.

LCM(514,522) = 134154

LCM of 514 and 522

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

LCM of:
and

Least Common Multiple of 514 and 522

LCM of 514 and 522 is 134154

Least common multiple can be found by multiplying the highest exponent prime factors of 514 and 522. First we will calculate the prime factors of 514 and 522.

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 522


2 522
3 261
3 87
29 29
1

Prime factors of 522 are 2, 3,29. Prime factorization of 522 in exponential form is:

522 = 21×32×291

Now multiplying the highest exponent prime factors to calculate the LCM of 514 and 522.

LCM(514,522) = 21×32×291×2571
LCM(514,522) = 134154

Factors of 514

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

1, 2, 257, 514

Factors of 522

List of positive integer factors of 522 that divides 522 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522

Least Common Multiple of 514 and 522 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 522, than apply into the LCM equation.

GCF(514,522) = 2
LCM(514,522) = ( 514 × 522) / 2
LCM(514,522) = 268308 / 2
LCM(514,522) = 134154

Properties of LCM 514 and 522

(i) The LCM of 522 and 514 is associative

LCM of 514 and 522 = LCM of 522 and 514

Related Least Common Multiples of 514

Related Least Common Multiples of 522

Frequently Asked Questions on LCM of 514 and 522

1. What is the LCM of 514 and 522?

Answer: LCM of 514 and 522 is 134154.

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 522?

Answer: Factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522. There are 12 integers that are factors of 522. The greatest factor of 522 is 522.

4. How to Find the LCM of 514 and 522?

Answer:

Least Common Multiple of 514 and 522 = 134154

Step 1: Find the prime factorization of 514

514 = 2 x 257

Step 2: Find the prime factorization of 522

522 = 2 x 3 x 3 x 29

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

LCM = 134154 = 2 x 3 x 3 x 29 x 257

Step 4: Therefore, the least common multiple of 514 and 522 is 134154.