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What is the Least Common Multiple of 54224 and 54240?

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 54224 and 54240 is 183819360.

LCM(54224,54240) = 183819360

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Least Common Multiple of 54224 and 54240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54224 and 54240, than apply into the LCM equation.

GCF(54224,54240) = 16
LCM(54224,54240) = ( 54224 × 54240) / 16
LCM(54224,54240) = 2941109760 / 16
LCM(54224,54240) = 183819360

Least Common Multiple (LCM) of 54224 and 54240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54224 and 54240. First we will calculate the prime factors of 54224 and 54240.

Prime Factorization of 54224

Prime factors of 54224 are 2, 3389. Prime factorization of 54224 in exponential form is:

54224 = 24 × 33891

Prime Factorization of 54240

Prime factors of 54240 are 2, 3, 5, 113. Prime factorization of 54240 in exponential form is:

54240 = 25 × 31 × 51 × 1131

Now multiplying the highest exponent prime factors to calculate the LCM of 54224 and 54240.

LCM(54224,54240) = 25 × 33891 × 31 × 51 × 1131
LCM(54224,54240) = 183819360