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What is the Least Common Multiple of 30198 and 30208?

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 30198 and 30208 is 456110592.

LCM(30198,30208) = 456110592

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Least Common Multiple of 30198 and 30208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30198 and 30208, than apply into the LCM equation.

GCF(30198,30208) = 2
LCM(30198,30208) = ( 30198 × 30208) / 2
LCM(30198,30208) = 912221184 / 2
LCM(30198,30208) = 456110592

Least Common Multiple (LCM) of 30198 and 30208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30198 and 30208. First we will calculate the prime factors of 30198 and 30208.

Prime Factorization of 30198

Prime factors of 30198 are 2, 3, 7, 719. Prime factorization of 30198 in exponential form is:

30198 = 21 × 31 × 71 × 7191

Prime Factorization of 30208

Prime factors of 30208 are 2, 59. Prime factorization of 30208 in exponential form is:

30208 = 29 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 30198 and 30208.

LCM(30198,30208) = 29 × 31 × 71 × 7191 × 591
LCM(30198,30208) = 456110592