Least Common Multiple of 1500 and 1508

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1500 and 1508 the smallest integer that is 565500 that is divisible by both numbers.

Least Common Multiple (LCM) of 1500 and 1508 is 565500.

LCM(1500,1508) = 565500

LCM of 1500 and 1508

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

LCM of:
and

Least Common Multiple of 1500 and 1508

LCM of 1500 and 1508 is 565500

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1508. First we will calculate the prime factors of 1500 and 1508.

Prime Factorization of 1500


2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 1500 are 2, 3,5. Prime factorization of 1500 in exponential form is:

1500 = 22×31×53

Prime Factorization of 1508


2 1508
2 754
13 377
29 29
1

Prime factors of 1508 are 2, 13,29. Prime factorization of 1508 in exponential form is:

1508 = 22×131×291

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1508.

LCM(1500,1508) = 22×31×53×131×291
LCM(1500,1508) = 565500

Factors of 1500

List of positive integer factors of 1500 that divides 1500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500

Factors of 1508

List of positive integer factors of 1508 that divides 1508 without a remainder.

1, 2, 4, 13, 26, 29, 52, 58, 116, 377, 754, 1508

Least Common Multiple of 1500 and 1508 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1500 and 1508, than apply into the LCM equation.

GCF(1500,1508) = 4
LCM(1500,1508) = ( 1500 × 1508) / 4
LCM(1500,1508) = 2262000 / 4
LCM(1500,1508) = 565500

Properties of LCM 1500 and 1508

(i) The LCM of 1508 and 1500 is associative

LCM of 1500 and 1508 = LCM of 1508 and 1500

Related Least Common Multiples of 1500

Related Least Common Multiples of 1508

Frequently Asked Questions on LCM of 1500 and 1508

1. What is the LCM of 1500 and 1508?

Answer: LCM of 1500 and 1508 is 565500.

2. What are the Factors of 1500?

Answer: Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500. There are 24 integers that are factors of 1500. The greatest factor of 1500 is 1500.

3. What are the Factors of 1508?

Answer: Factors of 1508 are 1, 2, 4, 13, 26, 29, 52, 58, 116, 377, 754, 1508. There are 12 integers that are factors of 1508. The greatest factor of 1508 is 1508.

4. How to Find the LCM of 1500 and 1508?

Answer:

Least Common Multiple of 1500 and 1508 = 565500

Step 1: Find the prime factorization of 1500

1500 = 2 x 2 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 1508

1508 = 2 x 2 x 13 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 = 565500 = 2 x 2 x 3 x 5 x 5 x 5 x 13 x 29

Step 4: Therefore, the least common multiple of 1500 and 1508 is 565500.