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What is the Least Common Multiple of 214 and 227?

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 214 and 227 is 48578.

LCM(214,227) = 48578

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Least Common Multiple of 214 and 227 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 214 and 227, than apply into the LCM equation.

GCF(214,227) = 1
LCM(214,227) = ( 214 × 227) / 1
LCM(214,227) = 48578 / 1
LCM(214,227) = 48578

Least Common Multiple (LCM) of 214 and 227 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 227. First we will calculate the prime factors of 214 and 227.

Prime Factorization of 214

Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:

214 = 21 × 1071

Prime Factorization of 227

Prime factors of 227 are 227. Prime factorization of 227 in exponential form is:

227 = 2271

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 227.

LCM(214,227) = 21 × 1071 × 2271
LCM(214,227) = 48578

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