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 2401 the smallest integer that is 5762400 that is divisible by both numbers.
Least Common Multiple (LCM) of 2400 and 2401 is 5762400.
LCM(2400,2401) = 5762400
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 2401. First we will calculate the prime factors of 2400 and 2401.
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 2401
7 | 2401 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 2401 are 7. Prime factorization of 2401 in exponential form is:
2401 = 74
Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2401.
LCM(2400,2401) = 25×31×52×74
LCM(2400,2401) = 5762400
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 2401
List of positive integer factors of 2401 that divides 2401 without a remainder.
1, 7, 49, 343, 2401
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2400 and 2401, than apply into the LCM equation.
GCF(2400,2401) = 1
LCM(2400,2401) = ( 2400 × 2401) / 1
LCM(2400,2401) = 5762400 / 1
LCM(2400,2401) = 5762400
(i) The LCM of 2401 and 2400 is associative
LCM of 2400 and 2401 = LCM of 2401 and 2400
1. What is the LCM of 2400 and 2401?
Answer: LCM of 2400 and 2401 is 5762400.
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 2401?
Answer: Factors of 2401 are 1, 7, 49, 343, 2401. There are 5 integers that are factors of 2401. The greatest factor of 2401 is 2401.
4. How to Find the LCM of 2400 and 2401?
Answer:
Least Common Multiple of 2400 and 2401 = 5762400
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 2401
2401 = 7 x 7 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5762400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 7 x 7 x 7
Step 4: Therefore, the least common multiple of 2400 and 2401 is 5762400.