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What is the Least Common Multiple of 214 and 230?

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 230 is 24610.

LCM(214,230) = 24610

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Least Common Multiple of 214 and 230 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 230, than apply into the LCM equation.

GCF(214,230) = 2
LCM(214,230) = ( 214 × 230) / 2
LCM(214,230) = 49220 / 2
LCM(214,230) = 24610

Least Common Multiple (LCM) of 214 and 230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 230. First we will calculate the prime factors of 214 and 230.

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 230

Prime factors of 230 are 2, 5, 23. Prime factorization of 230 in exponential form is:

230 = 21 × 51 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 230.

LCM(214,230) = 21 × 1071 × 51 × 231
LCM(214,230) = 24610

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