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What is the Least Common Multiple of 54888 and 54900?

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 54888 and 54900 is 251112600.

LCM(54888,54900) = 251112600

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Least Common Multiple of 54888 and 54900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54888 and 54900, than apply into the LCM equation.

GCF(54888,54900) = 12
LCM(54888,54900) = ( 54888 × 54900) / 12
LCM(54888,54900) = 3013351200 / 12
LCM(54888,54900) = 251112600

Least Common Multiple (LCM) of 54888 and 54900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54888 and 54900. First we will calculate the prime factors of 54888 and 54900.

Prime Factorization of 54888

Prime factors of 54888 are 2, 3, 2287. Prime factorization of 54888 in exponential form is:

54888 = 23 × 31 × 22871

Prime Factorization of 54900

Prime factors of 54900 are 2, 3, 5, 61. Prime factorization of 54900 in exponential form is:

54900 = 22 × 32 × 52 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 54888 and 54900.

LCM(54888,54900) = 23 × 32 × 22871 × 52 × 611
LCM(54888,54900) = 251112600