Least Common Multiple of 1500 and 1505

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 1505 the smallest integer that is 451500 that is divisible by both numbers.

Least Common Multiple (LCM) of 1500 and 1505 is 451500.

LCM(1500,1505) = 451500

LCM of 1500 and 1505

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

LCM of:
and

Least Common Multiple of 1500 and 1505

LCM of 1500 and 1505 is 451500

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1505. First we will calculate the prime factors of 1500 and 1505.

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 1505


5 1505
7 301
43 43
1

Prime factors of 1505 are 5, 7,43. Prime factorization of 1505 in exponential form is:

1505 = 51×71×431

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1505.

LCM(1500,1505) = 22×31×53×71×431
LCM(1500,1505) = 451500

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 1505

List of positive integer factors of 1505 that divides 1505 without a remainder.

1, 5, 7, 35, 43, 215, 301, 1505

Least Common Multiple of 1500 and 1505 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 1505, than apply into the LCM equation.

GCF(1500,1505) = 5
LCM(1500,1505) = ( 1500 × 1505) / 5
LCM(1500,1505) = 2257500 / 5
LCM(1500,1505) = 451500

Properties of LCM 1500 and 1505

(i) The LCM of 1505 and 1500 is associative

LCM of 1500 and 1505 = LCM of 1505 and 1500

Related Least Common Multiples of 1500

Related Least Common Multiples of 1505

Frequently Asked Questions on LCM of 1500 and 1505

1. What is the LCM of 1500 and 1505?

Answer: LCM of 1500 and 1505 is 451500.

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 1505?

Answer: Factors of 1505 are 1, 5, 7, 35, 43, 215, 301, 1505. There are 8 integers that are factors of 1505. The greatest factor of 1505 is 1505.

4. How to Find the LCM of 1500 and 1505?

Answer:

Least Common Multiple of 1500 and 1505 = 451500

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 1505

1505 = 5 x 7 x 43

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

LCM = 451500 = 2 x 2 x 3 x 5 x 5 x 5 x 7 x 43

Step 4: Therefore, the least common multiple of 1500 and 1505 is 451500.