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What is the Least Common Multiple of 2198 and 2208?

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 2198 and 2208 is 2426592.

LCM(2198,2208) = 2426592

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Least Common Multiple of 2198 and 2208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2198 and 2208, than apply into the LCM equation.

GCF(2198,2208) = 2
LCM(2198,2208) = ( 2198 × 2208) / 2
LCM(2198,2208) = 4853184 / 2
LCM(2198,2208) = 2426592

Least Common Multiple (LCM) of 2198 and 2208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2198 and 2208. First we will calculate the prime factors of 2198 and 2208.

Prime Factorization of 2198

Prime factors of 2198 are 2, 7, 157. Prime factorization of 2198 in exponential form is:

2198 = 21 × 71 × 1571

Prime Factorization of 2208

Prime factors of 2208 are 2, 3, 23. Prime factorization of 2208 in exponential form is:

2208 = 25 × 31 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 2198 and 2208.

LCM(2198,2208) = 25 × 71 × 1571 × 31 × 231
LCM(2198,2208) = 2426592