Least Common Multiple of 1500 and 1506

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 1506 the smallest integer that is 376500 that is divisible by both numbers.

Least Common Multiple (LCM) of 1500 and 1506 is 376500.

LCM(1500,1506) = 376500

LCM of 1500 and 1506

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

LCM of:
and

Least Common Multiple of 1500 and 1506

LCM of 1500 and 1506 is 376500

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1506. First we will calculate the prime factors of 1500 and 1506.

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 1506


2 1506
3 753
251 251
1

Prime factors of 1506 are 2, 3,251. Prime factorization of 1506 in exponential form is:

1506 = 21×31×2511

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1506.

LCM(1500,1506) = 22×31×53×2511
LCM(1500,1506) = 376500

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 1506

List of positive integer factors of 1506 that divides 1506 without a remainder.

1, 2, 3, 6, 251, 502, 753, 1506

Least Common Multiple of 1500 and 1506 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 1506, than apply into the LCM equation.

GCF(1500,1506) = 6
LCM(1500,1506) = ( 1500 × 1506) / 6
LCM(1500,1506) = 2259000 / 6
LCM(1500,1506) = 376500

Properties of LCM 1500 and 1506

(i) The LCM of 1506 and 1500 is associative

LCM of 1500 and 1506 = LCM of 1506 and 1500

Related Least Common Multiples of 1500

Related Least Common Multiples of 1506

Frequently Asked Questions on LCM of 1500 and 1506

1. What is the LCM of 1500 and 1506?

Answer: LCM of 1500 and 1506 is 376500.

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 1506?

Answer: Factors of 1506 are 1, 2, 3, 6, 251, 502, 753, 1506. There are 8 integers that are factors of 1506. The greatest factor of 1506 is 1506.

4. How to Find the LCM of 1500 and 1506?

Answer:

Least Common Multiple of 1500 and 1506 = 376500

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 1506

1506 = 2 x 3 x 251

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

LCM = 376500 = 2 x 2 x 3 x 5 x 5 x 5 x 251

Step 4: Therefore, the least common multiple of 1500 and 1506 is 376500.