Least Common Multiple of 516 and 523

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 516 and 523 the smallest integer that is 269868 that is divisible by both numbers.

Least Common Multiple (LCM) of 516 and 523 is 269868.

LCM(516,523) = 269868

LCM of 516 and 523

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

LCM of:
and

Least Common Multiple of 516 and 523

LCM of 516 and 523 is 269868

Least common multiple can be found by multiplying the highest exponent prime factors of 516 and 523. First we will calculate the prime factors of 516 and 523.

Prime Factorization of 516


2 516
2 258
3 129
43 43
1

Prime factors of 516 are 2, 3,43. Prime factorization of 516 in exponential form is:

516 = 22×31×431

Prime Factorization of 523


523 523
1

Prime factors of 523 are 523. Prime factorization of 523 in exponential form is:

523 = 5231

Now multiplying the highest exponent prime factors to calculate the LCM of 516 and 523.

LCM(516,523) = 22×31×431×5231
LCM(516,523) = 269868

Factors of 516

List of positive integer factors of 516 that divides 516 without a remainder.

1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516

Factors of 523

List of positive integer factors of 523 that divides 523 without a remainder.

1, 523

Least Common Multiple of 516 and 523 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 516 and 523, than apply into the LCM equation.

GCF(516,523) = 1
LCM(516,523) = ( 516 × 523) / 1
LCM(516,523) = 269868 / 1
LCM(516,523) = 269868

Properties of LCM 516 and 523

(i) The LCM of 523 and 516 is associative

LCM of 516 and 523 = LCM of 523 and 516

Related Least Common Multiples of 516

Related Least Common Multiples of 523

Frequently Asked Questions on LCM of 516 and 523

1. What is the LCM of 516 and 523?

Answer: LCM of 516 and 523 is 269868.

2. What are the Factors of 516?

Answer: Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516. There are 12 integers that are factors of 516. The greatest factor of 516 is 516.

3. What are the Factors of 523?

Answer: Factors of 523 are 1, 523. There are 2 integers that are factors of 523. The greatest factor of 523 is 523.

4. How to Find the LCM of 516 and 523?

Answer:

Least Common Multiple of 516 and 523 = 269868

Step 1: Find the prime factorization of 516

516 = 2 x 2 x 3 x 43

Step 2: Find the prime factorization of 523

523 = 523

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

LCM = 269868 = 2 x 2 x 3 x 43 x 523

Step 4: Therefore, the least common multiple of 516 and 523 is 269868.