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What is the Least Common Multiple of 8414 and 8428?

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 8414 and 8428 is 5065228.

LCM(8414,8428) = 5065228

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Least Common Multiple of 8414 and 8428 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8414 and 8428, than apply into the LCM equation.

GCF(8414,8428) = 14
LCM(8414,8428) = ( 8414 × 8428) / 14
LCM(8414,8428) = 70913192 / 14
LCM(8414,8428) = 5065228

Least Common Multiple (LCM) of 8414 and 8428 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8414 and 8428. First we will calculate the prime factors of 8414 and 8428.

Prime Factorization of 8414

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

8414 = 21 × 71 × 6011

Prime Factorization of 8428

Prime factors of 8428 are 2, 7, 43. Prime factorization of 8428 in exponential form is:

8428 = 22 × 72 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 8414 and 8428.

LCM(8414,8428) = 22 × 72 × 6011 × 431
LCM(8414,8428) = 5065228