Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2500 and 2504 the smallest integer that is 1565000 that is divisible by both numbers.
Least Common Multiple (LCM) of 2500 and 2504 is 1565000.
LCM(2500,2504) = 1565000
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 2500 and 2504. First we will calculate the prime factors of 2500 and 2504.
Prime Factorization of 2500
2 | 2500 |
2 | 1250 |
5 | 625 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 2500 are 2,5. Prime factorization of 2500 in exponential form is:
2500 = 22×54
Prime Factorization of 2504
2 | 2504 |
2 | 1252 |
2 | 626 |
313 | 313 |
1 |
Prime factors of 2504 are 2,313. Prime factorization of 2504 in exponential form is:
2504 = 23×3131
Now multiplying the highest exponent prime factors to calculate the LCM of 2500 and 2504.
LCM(2500,2504) = 23×54×3131
LCM(2500,2504) = 1565000
Factors of 2500
List of positive integer factors of 2500 that divides 2500 without a remainder.
1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500
Factors of 2504
List of positive integer factors of 2504 that divides 2504 without a remainder.
1, 2, 4, 8, 313, 626, 1252, 2504
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2500 and 2504, than apply into the LCM equation.
GCF(2500,2504) = 4
LCM(2500,2504) = ( 2500 × 2504) / 4
LCM(2500,2504) = 6260000 / 4
LCM(2500,2504) = 1565000
(i) The LCM of 2504 and 2500 is associative
LCM of 2500 and 2504 = LCM of 2504 and 2500
1. What is the LCM of 2500 and 2504?
Answer: LCM of 2500 and 2504 is 1565000.
2. What are the Factors of 2500?
Answer: Factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500. There are 15 integers that are factors of 2500. The greatest factor of 2500 is 2500.
3. What are the Factors of 2504?
Answer: Factors of 2504 are 1, 2, 4, 8, 313, 626, 1252, 2504. There are 8 integers that are factors of 2504. The greatest factor of 2504 is 2504.
4. How to Find the LCM of 2500 and 2504?
Answer:
Least Common Multiple of 2500 and 2504 = 1565000
Step 1: Find the prime factorization of 2500
2500 = 2 x 2 x 5 x 5 x 5 x 5
Step 2: Find the prime factorization of 2504
2504 = 2 x 2 x 2 x 313
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1565000 = 2 x 2 x 2 x 5 x 5 x 5 x 5 x 313
Step 4: Therefore, the least common multiple of 2500 and 2504 is 1565000.