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What is the Least Common Multiple of 30208 and 30224?

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 30208 and 30224 is 57062912.

LCM(30208,30224) = 57062912

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Least Common Multiple of 30208 and 30224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30208 and 30224, than apply into the LCM equation.

GCF(30208,30224) = 16
LCM(30208,30224) = ( 30208 × 30224) / 16
LCM(30208,30224) = 913006592 / 16
LCM(30208,30224) = 57062912

Least Common Multiple (LCM) of 30208 and 30224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30208 and 30224. First we will calculate the prime factors of 30208 and 30224.

Prime Factorization of 30208

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

30208 = 29 × 591

Prime Factorization of 30224

Prime factors of 30224 are 2, 1889. Prime factorization of 30224 in exponential form is:

30224 = 24 × 18891

Now multiplying the highest exponent prime factors to calculate the LCM of 30208 and 30224.

LCM(30208,30224) = 29 × 591 × 18891
LCM(30208,30224) = 57062912