Least Common Multiple of 500 and 506

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 500 and 506 the smallest integer that is 126500 that is divisible by both numbers.

Least Common Multiple (LCM) of 500 and 506 is 126500.

LCM(500,506) = 126500

LCM of 500 and 506

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

LCM of:
and

Least Common Multiple of 500 and 506

LCM of 500 and 506 is 126500

Least common multiple can be found by multiplying the highest exponent prime factors of 500 and 506. First we will calculate the prime factors of 500 and 506.

Prime Factorization of 500


2 500
2 250
5 125
5 25
5 5
1

Prime factors of 500 are 2,5. Prime factorization of 500 in exponential form is:

500 = 22×53

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

Now multiplying the highest exponent prime factors to calculate the LCM of 500 and 506.

LCM(500,506) = 22×53×111×231
LCM(500,506) = 126500

Factors of 500

List of positive integer factors of 500 that divides 500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

Factors of 506

List of positive integer factors of 506 that divides 506 without a remainder.

1, 2, 11, 22, 23, 46, 253, 506

Least Common Multiple of 500 and 506 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 500 and 506, than apply into the LCM equation.

GCF(500,506) = 2
LCM(500,506) = ( 500 × 506) / 2
LCM(500,506) = 253000 / 2
LCM(500,506) = 126500

Properties of LCM 500 and 506

(i) The LCM of 506 and 500 is associative

LCM of 500 and 506 = LCM of 506 and 500

Related Least Common Multiples of 500

Related Least Common Multiples of 506

Frequently Asked Questions on LCM of 500 and 506

1. What is the LCM of 500 and 506?

Answer: LCM of 500 and 506 is 126500.

2. What are the Factors of 500?

Answer: Factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500. There are 12 integers that are factors of 500. The greatest factor of 500 is 500.

3. 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.

4. How to Find the LCM of 500 and 506?

Answer:

Least Common Multiple of 500 and 506 = 126500

Step 1: Find the prime factorization of 500

500 = 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 506

506 = 2 x 11 x 23

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

LCM = 126500 = 2 x 2 x 5 x 5 x 5 x 11 x 23

Step 4: Therefore, the least common multiple of 500 and 506 is 126500.