Least Common Multiple of 500 and 505

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 505 the smallest integer that is 50500 that is divisible by both numbers.

Least Common Multiple (LCM) of 500 and 505 is 50500.

LCM(500,505) = 50500

LCM of 500 and 505

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

LCM of:
and

Least Common Multiple of 500 and 505

LCM of 500 and 505 is 50500

Least common multiple can be found by multiplying the highest exponent prime factors of 500 and 505. First we will calculate the prime factors of 500 and 505.

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 505


5 505
101 101
1

Prime factors of 505 are 5,101. Prime factorization of 505 in exponential form is:

505 = 51×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 500 and 505.

LCM(500,505) = 22×53×1011
LCM(500,505) = 50500

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 505

List of positive integer factors of 505 that divides 505 without a remainder.

1, 5, 101, 505

Least Common Multiple of 500 and 505 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 505, than apply into the LCM equation.

GCF(500,505) = 5
LCM(500,505) = ( 500 × 505) / 5
LCM(500,505) = 252500 / 5
LCM(500,505) = 50500

Properties of LCM 500 and 505

(i) The LCM of 505 and 500 is associative

LCM of 500 and 505 = LCM of 505 and 500

Related Least Common Multiples of 500

Related Least Common Multiples of 505

Frequently Asked Questions on LCM of 500 and 505

1. What is the LCM of 500 and 505?

Answer: LCM of 500 and 505 is 50500.

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 505?

Answer: Factors of 505 are 1, 5, 101, 505. There are 4 integers that are factors of 505. The greatest factor of 505 is 505.

4. How to Find the LCM of 500 and 505?

Answer:

Least Common Multiple of 500 and 505 = 50500

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 505

505 = 5 x 101

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

LCM = 50500 = 2 x 2 x 5 x 5 x 5 x 101

Step 4: Therefore, the least common multiple of 500 and 505 is 50500.