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What is the Least Common Multiple of 214 and 218?

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 218 is 23326.

LCM(214,218) = 23326

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Least Common Multiple of 214 and 218 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 218, than apply into the LCM equation.

GCF(214,218) = 2
LCM(214,218) = ( 214 × 218) / 2
LCM(214,218) = 46652 / 2
LCM(214,218) = 23326

Least Common Multiple (LCM) of 214 and 218 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 218. First we will calculate the prime factors of 214 and 218.

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 218

Prime factors of 218 are 2, 109. Prime factorization of 218 in exponential form is:

218 = 21 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 218.

LCM(214,218) = 21 × 1071 × 1091
LCM(214,218) = 23326

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