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What is the Least Common Multiple of 8398 and 8414?

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 8398 and 8414 is 35330386.

LCM(8398,8414) = 35330386

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Least Common Multiple of 8398 and 8414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8398 and 8414, than apply into the LCM equation.

GCF(8398,8414) = 2
LCM(8398,8414) = ( 8398 × 8414) / 2
LCM(8398,8414) = 70660772 / 2
LCM(8398,8414) = 35330386

Least Common Multiple (LCM) of 8398 and 8414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8398 and 8414. First we will calculate the prime factors of 8398 and 8414.

Prime Factorization of 8398

Prime factors of 8398 are 2, 13, 17, 19. Prime factorization of 8398 in exponential form is:

8398 = 21 × 131 × 171 × 191

Prime Factorization of 8414

Prime factors of 8414 are 2, 7, 601. Prime factorization of 8414 in exponential form is:

8414 = 21 × 71 × 6011

Now multiplying the highest exponent prime factors to calculate the LCM of 8398 and 8414.

LCM(8398,8414) = 21 × 131 × 171 × 191 × 71 × 6011
LCM(8398,8414) = 35330386