Least Common Multiple of 7500 and 7504

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7500 and 7504 the smallest integer that is 14070000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7500 and 7504 is 14070000.

LCM(7500,7504) = 14070000

LCM of 7500 and 7504

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

LCM of:
and

Least Common Multiple of 7500 and 7504

LCM of 7500 and 7504 is 14070000

Least common multiple can be found by multiplying the highest exponent prime factors of 7500 and 7504. First we will calculate the prime factors of 7500 and 7504.

Prime Factorization of 7500


2 7500
2 3750
3 1875
5 625
5 125
5 25
5 5
1

Prime factors of 7500 are 2, 3,5. Prime factorization of 7500 in exponential form is:

7500 = 22×31×54

Prime Factorization of 7504


2 7504
2 3752
2 1876
2 938
7 469
67 67
1

Prime factors of 7504 are 2, 7,67. Prime factorization of 7504 in exponential form is:

7504 = 24×71×671

Now multiplying the highest exponent prime factors to calculate the LCM of 7500 and 7504.

LCM(7500,7504) = 24×31×54×71×671
LCM(7500,7504) = 14070000

Factors of 7500

List of positive integer factors of 7500 that divides 7500 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, 625, 750, 1250, 1500, 1875, 2500, 3750, 7500

Factors of 7504

List of positive integer factors of 7504 that divides 7504 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 67, 112, 134, 268, 469, 536, 938, 1072, 1876, 3752, 7504

Least Common Multiple of 7500 and 7504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7500 and 7504, than apply into the LCM equation.

GCF(7500,7504) = 4
LCM(7500,7504) = ( 7500 × 7504) / 4
LCM(7500,7504) = 56280000 / 4
LCM(7500,7504) = 14070000

Properties of LCM 7500 and 7504

(i) The LCM of 7504 and 7500 is associative

LCM of 7500 and 7504 = LCM of 7504 and 7500

Related Least Common Multiples of 7500

Related Least Common Multiples of 7504

Frequently Asked Questions on LCM of 7500 and 7504

1. What is the LCM of 7500 and 7504?

Answer: LCM of 7500 and 7504 is 14070000.

2. What are the Factors of 7500?

Answer: Factors of 7500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 625, 750, 1250, 1500, 1875, 2500, 3750, 7500. There are 30 integers that are factors of 7500. The greatest factor of 7500 is 7500.

3. What are the Factors of 7504?

Answer: Factors of 7504 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 67, 112, 134, 268, 469, 536, 938, 1072, 1876, 3752, 7504. There are 20 integers that are factors of 7504. The greatest factor of 7504 is 7504.

4. How to Find the LCM of 7500 and 7504?

Answer:

Least Common Multiple of 7500 and 7504 = 14070000

Step 1: Find the prime factorization of 7500

7500 = 2 x 2 x 3 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 7504

7504 = 2 x 2 x 2 x 2 x 7 x 67

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

LCM = 14070000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 7 x 67

Step 4: Therefore, the least common multiple of 7500 and 7504 is 14070000.