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What is the Least Common Multiple of 214 and 231?

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 231 is 49434.

LCM(214,231) = 49434

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Least Common Multiple of 214 and 231 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 231, than apply into the LCM equation.

GCF(214,231) = 1
LCM(214,231) = ( 214 × 231) / 1
LCM(214,231) = 49434 / 1
LCM(214,231) = 49434

Least Common Multiple (LCM) of 214 and 231 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 231. First we will calculate the prime factors of 214 and 231.

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 231

Prime factors of 231 are 3, 7, 11. Prime factorization of 231 in exponential form is:

231 = 31 × 71 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 231.

LCM(214,231) = 21 × 1071 × 31 × 71 × 111
LCM(214,231) = 49434

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