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What is the Least Common Multiple of 214 and 219?

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 219 is 46866.

LCM(214,219) = 46866

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Least Common Multiple of 214 and 219 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 219, than apply into the LCM equation.

GCF(214,219) = 1
LCM(214,219) = ( 214 × 219) / 1
LCM(214,219) = 46866 / 1
LCM(214,219) = 46866

Least Common Multiple (LCM) of 214 and 219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 219. First we will calculate the prime factors of 214 and 219.

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 219

Prime factors of 219 are 3, 73. Prime factorization of 219 in exponential form is:

219 = 31 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 219.

LCM(214,219) = 21 × 1071 × 31 × 731
LCM(214,219) = 46866

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