Least Common Multiple of 2408 and 2414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2408 and 2414 the smallest integer that is 2906456 that is divisible by both numbers.

Least Common Multiple (LCM) of 2408 and 2414 is 2906456.

LCM(2408,2414) = 2906456

LCM of 2408 and 2414

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

LCM of:
and

Least Common Multiple of 2408 and 2414

LCM of 2408 and 2414 is 2906456

Least common multiple can be found by multiplying the highest exponent prime factors of 2408 and 2414. First we will calculate the prime factors of 2408 and 2414.

Prime Factorization of 2408


2 2408
2 1204
2 602
7 301
43 43
1

Prime factors of 2408 are 2, 7,43. Prime factorization of 2408 in exponential form is:

2408 = 23×71×431

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 2408 and 2414.

LCM(2408,2414) = 23×71×171×431×711
LCM(2408,2414) = 2906456

Factors of 2408

List of positive integer factors of 2408 that divides 2408 without a remainder.

1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408

Factors of 2414

List of positive integer factors of 2414 that divides 2414 without a remainder.

1, 2, 17, 34, 71, 142, 1207, 2414

Least Common Multiple of 2408 and 2414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2408 and 2414, than apply into the LCM equation.

GCF(2408,2414) = 2
LCM(2408,2414) = ( 2408 × 2414) / 2
LCM(2408,2414) = 5812912 / 2
LCM(2408,2414) = 2906456

Properties of LCM 2408 and 2414

(i) The LCM of 2414 and 2408 is associative

LCM of 2408 and 2414 = LCM of 2414 and 2408

Related Least Common Multiples of 2408

Related Least Common Multiples of 2414

Frequently Asked Questions on LCM of 2408 and 2414

1. What is the LCM of 2408 and 2414?

Answer: LCM of 2408 and 2414 is 2906456.

2. What are the Factors of 2408?

Answer: Factors of 2408 are 1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408. There are 16 integers that are factors of 2408. The greatest factor of 2408 is 2408.

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 2408 and 2414?

Answer:

Least Common Multiple of 2408 and 2414 = 2906456

Step 1: Find the prime factorization of 2408

2408 = 2 x 2 x 2 x 7 x 43

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 = 2906456 = 2 x 2 x 2 x 7 x 17 x 43 x 71

Step 4: Therefore, the least common multiple of 2408 and 2414 is 2906456.