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What is the Least Common Multiple of 219 and 238?

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 219 and 238 is 52122.

LCM(219,238) = 52122

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Least Common Multiple of 219 and 238 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 219 and 238, than apply into the LCM equation.

GCF(219,238) = 1
LCM(219,238) = ( 219 × 238) / 1
LCM(219,238) = 52122 / 1
LCM(219,238) = 52122

Least Common Multiple (LCM) of 219 and 238 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 219 and 238. First we will calculate the prime factors of 219 and 238.

Prime Factorization of 219

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

219 = 31 × 731

Prime Factorization of 238

Prime factors of 238 are 2, 7, 17. Prime factorization of 238 in exponential form is:

238 = 21 × 71 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 219 and 238.

LCM(219,238) = 31 × 731 × 21 × 71 × 171
LCM(219,238) = 52122

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