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What is the Least Common Multiple of 54198 and 54208?

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 54198 and 54208 is 1468982592.

LCM(54198,54208) = 1468982592

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Least Common Multiple of 54198 and 54208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54198 and 54208, than apply into the LCM equation.

GCF(54198,54208) = 2
LCM(54198,54208) = ( 54198 × 54208) / 2
LCM(54198,54208) = 2937965184 / 2
LCM(54198,54208) = 1468982592

Least Common Multiple (LCM) of 54198 and 54208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54198 and 54208. First we will calculate the prime factors of 54198 and 54208.

Prime Factorization of 54198

Prime factors of 54198 are 2, 3, 3011. Prime factorization of 54198 in exponential form is:

54198 = 21 × 32 × 30111

Prime Factorization of 54208

Prime factors of 54208 are 2, 7, 11. Prime factorization of 54208 in exponential form is:

54208 = 26 × 71 × 112

Now multiplying the highest exponent prime factors to calculate the LCM of 54198 and 54208.

LCM(54198,54208) = 26 × 32 × 30111 × 71 × 112
LCM(54198,54208) = 1468982592