What is the Least Common Multiple of 54800 and 54816?
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 54800 and 54816 is 187744800.
LCM(54800,54816) = 187744800
Least Common Multiple of 54800 and 54816 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54800 and 54816, than apply into the LCM equation.
GCF(54800,54816) = 16
LCM(54800,54816) = ( 54800 × 54816) / 16
LCM(54800,54816) = 3003916800 / 16
LCM(54800,54816) = 187744800
Least Common Multiple (LCM) of 54800 and 54816 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 54800 and 54816. First we will calculate the prime factors of 54800 and 54816.
Prime Factorization of 54800
Prime factors of 54800 are 2, 5, 137. Prime factorization of 54800 in exponential form is:
54800 = 24 × 52 × 1371
Prime Factorization of 54816
Prime factors of 54816 are 2, 3, 571. Prime factorization of 54816 in exponential form is:
54816 = 25 × 31 × 5711
Now multiplying the highest exponent prime factors to calculate the LCM of 54800 and 54816.
LCM(54800,54816) = 25 × 52 × 1371 × 31 × 5711
LCM(54800,54816) = 187744800
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