Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2407 and 2414 the smallest integer that is 5810498 that is divisible by both numbers.
Least Common Multiple (LCM) of 2407 and 2414 is 5810498.
LCM(2407,2414) = 5810498
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 2407 and 2414. First we will calculate the prime factors of 2407 and 2414.
Prime Factorization of 2407
29 | 2407 |
83 | 83 |
1 |
Prime factors of 2407 are 29,83. Prime factorization of 2407 in exponential form is:
2407 = 291×831
Prime Factorization of 2414
2 | 2414 |
17 | 1207 |
71 | 71 |
1 |
Prime factors of 2414 are 2, 17,71. Prime factorization of 2414 in exponential form is:
2414 = 21×171×711
Now multiplying the highest exponent prime factors to calculate the LCM of 2407 and 2414.
LCM(2407,2414) = 21×171×291×711×831
LCM(2407,2414) = 5810498
Factors of 2407
List of positive integer factors of 2407 that divides 2407 without a remainder.
1, 29, 83, 2407
Factors of 2414
List of positive integer factors of 2414 that divides 2414 without a remainder.
1, 2, 17, 34, 71, 142, 1207, 2414
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2407 and 2414, than apply into the LCM equation.
GCF(2407,2414) = 1
LCM(2407,2414) = ( 2407 × 2414) / 1
LCM(2407,2414) = 5810498 / 1
LCM(2407,2414) = 5810498
(i) The LCM of 2414 and 2407 is associative
LCM of 2407 and 2414 = LCM of 2414 and 2407
1. What is the LCM of 2407 and 2414?
Answer: LCM of 2407 and 2414 is 5810498.
2. What are the Factors of 2407?
Answer: Factors of 2407 are 1, 29, 83, 2407. There are 4 integers that are factors of 2407. The greatest factor of 2407 is 2407.
3. What are the Factors of 2414?
Answer: Factors of 2414 are 1, 2, 17, 34, 71, 142, 1207, 2414. There are 8 integers that are factors of 2414. The greatest factor of 2414 is 2414.
4. How to Find the LCM of 2407 and 2414?
Answer:
Least Common Multiple of 2407 and 2414 = 5810498
Step 1: Find the prime factorization of 2407
2407 = 29 x 83
Step 2: Find the prime factorization of 2414
2414 = 2 x 17 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5810498 = 2 x 17 x 29 x 71 x 83
Step 4: Therefore, the least common multiple of 2407 and 2414 is 5810498.