Least Common Multiple of 1500 and 1504

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 1504 the smallest integer that is 564000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1500 and 1504 is 564000.

LCM(1500,1504) = 564000

LCM of 1500 and 1504

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

LCM of:
and

Least Common Multiple of 1500 and 1504

LCM of 1500 and 1504 is 564000

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1504. First we will calculate the prime factors of 1500 and 1504.

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 1504


2 1504
2 752
2 376
2 188
2 94
47 47
1

Prime factors of 1504 are 2,47. Prime factorization of 1504 in exponential form is:

1504 = 25×471

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1504.

LCM(1500,1504) = 25×31×53×471
LCM(1500,1504) = 564000

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 1504

List of positive integer factors of 1504 that divides 1504 without a remainder.

1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504

Least Common Multiple of 1500 and 1504 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 1504, than apply into the LCM equation.

GCF(1500,1504) = 4
LCM(1500,1504) = ( 1500 × 1504) / 4
LCM(1500,1504) = 2256000 / 4
LCM(1500,1504) = 564000

Properties of LCM 1500 and 1504

(i) The LCM of 1504 and 1500 is associative

LCM of 1500 and 1504 = LCM of 1504 and 1500

Related Least Common Multiples of 1500

Related Least Common Multiples of 1504

Frequently Asked Questions on LCM of 1500 and 1504

1. What is the LCM of 1500 and 1504?

Answer: LCM of 1500 and 1504 is 564000.

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 1504?

Answer: Factors of 1504 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504. There are 12 integers that are factors of 1504. The greatest factor of 1504 is 1504.

4. How to Find the LCM of 1500 and 1504?

Answer:

Least Common Multiple of 1500 and 1504 = 564000

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 1504

1504 = 2 x 2 x 2 x 2 x 2 x 47

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

LCM = 564000 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 47

Step 4: Therefore, the least common multiple of 1500 and 1504 is 564000.