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What is the Least Common Multiple of 198 and 208?

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 208 is 20592.

LCM(198,208) = 20592

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Least Common Multiple of 198 and 208 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 208, than apply into the LCM equation.

GCF(198,208) = 2
LCM(198,208) = ( 198 × 208) / 2
LCM(198,208) = 41184 / 2
LCM(198,208) = 20592

Least Common Multiple (LCM) of 198 and 208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 208. First we will calculate the prime factors of 198 and 208.

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 208

Prime factors of 208 are 2, 13. Prime factorization of 208 in exponential form is:

208 = 24 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 208.

LCM(198,208) = 24 × 32 × 111 × 131
LCM(198,208) = 20592

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