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What is the Least Common Multiple of 2398 and 2414?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 2398 and 2414 is 2894386.

LCM(2398,2414) = 2894386

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Least Common Multiple of 2398 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 2398 and 2414, than apply into the LCM equation.

GCF(2398,2414) = 2
LCM(2398,2414) = ( 2398 × 2414) / 2
LCM(2398,2414) = 5788772 / 2
LCM(2398,2414) = 2894386

Least Common Multiple (LCM) of 2398 and 2414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2398 and 2414. First we will calculate the prime factors of 2398 and 2414.

Prime Factorization of 2398

Prime factors of 2398 are 2, 11, 109. Prime factorization of 2398 in exponential form is:

2398 = 21 × 111 × 1091

Prime Factorization of 2414

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 2398 and 2414.

LCM(2398,2414) = 21 × 111 × 1091 × 171 × 711
LCM(2398,2414) = 2894386