Least Common Multiple of 1500 and 1507

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 1507 the smallest integer that is 2260500 that is divisible by both numbers.

Least Common Multiple (LCM) of 1500 and 1507 is 2260500.

LCM(1500,1507) = 2260500

LCM of 1500 and 1507

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

LCM of:
and

Least Common Multiple of 1500 and 1507

LCM of 1500 and 1507 is 2260500

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1507. First we will calculate the prime factors of 1500 and 1507.

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 1507


11 1507
137 137
1

Prime factors of 1507 are 11,137. Prime factorization of 1507 in exponential form is:

1507 = 111×1371

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1507.

LCM(1500,1507) = 22×31×53×111×1371
LCM(1500,1507) = 2260500

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 1507

List of positive integer factors of 1507 that divides 1507 without a remainder.

1, 11, 137, 1507

Least Common Multiple of 1500 and 1507 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 1507, than apply into the LCM equation.

GCF(1500,1507) = 1
LCM(1500,1507) = ( 1500 × 1507) / 1
LCM(1500,1507) = 2260500 / 1
LCM(1500,1507) = 2260500

Properties of LCM 1500 and 1507

(i) The LCM of 1507 and 1500 is associative

LCM of 1500 and 1507 = LCM of 1507 and 1500

Related Least Common Multiples of 1500

Related Least Common Multiples of 1507

Frequently Asked Questions on LCM of 1500 and 1507

1. What is the LCM of 1500 and 1507?

Answer: LCM of 1500 and 1507 is 2260500.

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 1507?

Answer: Factors of 1507 are 1, 11, 137, 1507. There are 4 integers that are factors of 1507. The greatest factor of 1507 is 1507.

4. How to Find the LCM of 1500 and 1507?

Answer:

Least Common Multiple of 1500 and 1507 = 2260500

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 1507

1507 = 11 x 137

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

LCM = 2260500 = 2 x 2 x 3 x 5 x 5 x 5 x 11 x 137

Step 4: Therefore, the least common multiple of 1500 and 1507 is 2260500.