Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2400 and 2404 the smallest integer that is 1442400 that is divisible by both numbers.
Least Common Multiple (LCM) of 2400 and 2404 is 1442400.
LCM(2400,2404) = 1442400
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 2400 and 2404. First we will calculate the prime factors of 2400 and 2404.
Prime Factorization of 2400
2 | 2400 |
2 | 1200 |
2 | 600 |
2 | 300 |
2 | 150 |
3 | 75 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 2400 are 2, 3,5. Prime factorization of 2400 in exponential form is:
2400 = 25×31×52
Prime Factorization of 2404
2 | 2404 |
2 | 1202 |
601 | 601 |
1 |
Prime factors of 2404 are 2,601. Prime factorization of 2404 in exponential form is:
2404 = 22×6011
Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2404.
LCM(2400,2404) = 25×31×52×6011
LCM(2400,2404) = 1442400
Factors of 2400
List of positive integer factors of 2400 that divides 2400 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400
Factors of 2404
List of positive integer factors of 2404 that divides 2404 without a remainder.
1, 2, 4, 601, 1202, 2404
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2400 and 2404, than apply into the LCM equation.
GCF(2400,2404) = 4
LCM(2400,2404) = ( 2400 × 2404) / 4
LCM(2400,2404) = 5769600 / 4
LCM(2400,2404) = 1442400
(i) The LCM of 2404 and 2400 is associative
LCM of 2400 and 2404 = LCM of 2404 and 2400
1. What is the LCM of 2400 and 2404?
Answer: LCM of 2400 and 2404 is 1442400.
2. What are the Factors of 2400?
Answer: Factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400. There are 36 integers that are factors of 2400. The greatest factor of 2400 is 2400.
3. What are the Factors of 2404?
Answer: Factors of 2404 are 1, 2, 4, 601, 1202, 2404. There are 6 integers that are factors of 2404. The greatest factor of 2404 is 2404.
4. How to Find the LCM of 2400 and 2404?
Answer:
Least Common Multiple of 2400 and 2404 = 1442400
Step 1: Find the prime factorization of 2400
2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
Step 2: Find the prime factorization of 2404
2404 = 2 x 2 x 601
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1442400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 601
Step 4: Therefore, the least common multiple of 2400 and 2404 is 1442400.