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Least Common Multiple of 198 and 217

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 198 and 217 is 42966.

LCM(198,217) = 42966

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Least Common Multiple of 198 and 217 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 198 and 217, than apply into the LCM equation.

GCF(198,217) = 1
LCM(198,217) = ( 198 × 217) / 1
LCM(198,217) = 42966 / 1
LCM(198,217) = 42966

Least Common Multiple (LCM) of 198 and 217 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 217. First we will calculate the prime factors of 198 and 217.

Prime Factorization of 198

Prime factors of 198 are 2, 3, 11. Prime factorization of 198 in exponential form is:

198 = 21 × 32 × 111

Prime Factorization of 217

Prime factors of 217 are 7, 31. Prime factorization of 217 in exponential form is:

217 = 71 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 217.

LCM(198,217) = 21 × 32 × 111 × 71 × 311
LCM(198,217) = 42966

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