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Least Common Multiple of 198 and 209

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 209 is 3762.

LCM(198,209) = 3762

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Least Common Multiple of 198 and 209 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 209, than apply into the LCM equation.

GCF(198,209) = 11
LCM(198,209) = ( 198 × 209) / 11
LCM(198,209) = 41382 / 11
LCM(198,209) = 3762

Least Common Multiple (LCM) of 198 and 209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 209. First we will calculate the prime factors of 198 and 209.

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 209

Prime factors of 209 are 11, 19. Prime factorization of 209 in exponential form is:

209 = 111 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 209.

LCM(198,209) = 21 × 32 × 111 × 191
LCM(198,209) = 3762

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