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What is the Least Common Multiple of 214 and 234?

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 234 is 25038.

LCM(214,234) = 25038

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Least Common Multiple of 214 and 234 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 234, than apply into the LCM equation.

GCF(214,234) = 2
LCM(214,234) = ( 214 × 234) / 2
LCM(214,234) = 50076 / 2
LCM(214,234) = 25038

Least Common Multiple (LCM) of 214 and 234 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 234. First we will calculate the prime factors of 214 and 234.

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 234

Prime factors of 234 are 2, 3, 13. Prime factorization of 234 in exponential form is:

234 = 21 × 32 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 234.

LCM(214,234) = 21 × 1071 × 32 × 131
LCM(214,234) = 25038

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