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What is the Least Common Multiple of 4205 and 4214?

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 4205 and 4214 is 17719870.

LCM(4205,4214) = 17719870

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Least Common Multiple of 4205 and 4214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4205 and 4214, than apply into the LCM equation.

GCF(4205,4214) = 1
LCM(4205,4214) = ( 4205 × 4214) / 1
LCM(4205,4214) = 17719870 / 1
LCM(4205,4214) = 17719870

Least Common Multiple (LCM) of 4205 and 4214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4205 and 4214. First we will calculate the prime factors of 4205 and 4214.

Prime Factorization of 4205

Prime factors of 4205 are 5, 29. Prime factorization of 4205 in exponential form is:

4205 = 51 × 292

Prime Factorization of 4214

Prime factors of 4214 are 2, 7, 43. Prime factorization of 4214 in exponential form is:

4214 = 21 × 72 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 4205 and 4214.

LCM(4205,4214) = 51 × 292 × 21 × 72 × 431
LCM(4205,4214) = 17719870