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What is the Least Common Multiple of 54708 and 54720?

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 54708 and 54720 is 249468480.

LCM(54708,54720) = 249468480

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Least Common Multiple of 54708 and 54720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54708 and 54720, than apply into the LCM equation.

GCF(54708,54720) = 12
LCM(54708,54720) = ( 54708 × 54720) / 12
LCM(54708,54720) = 2993621760 / 12
LCM(54708,54720) = 249468480

Least Common Multiple (LCM) of 54708 and 54720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54708 and 54720. First we will calculate the prime factors of 54708 and 54720.

Prime Factorization of 54708

Prime factors of 54708 are 2, 3, 47, 97. Prime factorization of 54708 in exponential form is:

54708 = 22 × 31 × 471 × 971

Prime Factorization of 54720

Prime factors of 54720 are 2, 3, 5, 19. Prime factorization of 54720 in exponential form is:

54720 = 26 × 32 × 51 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 54708 and 54720.

LCM(54708,54720) = 26 × 32 × 471 × 971 × 51 × 191
LCM(54708,54720) = 249468480