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What is the Least Common Multiple of 54999 and 55005?

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 54999 and 55005 is 1008406665.

LCM(54999,55005) = 1008406665

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Least Common Multiple of 54999 and 55005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54999 and 55005, than apply into the LCM equation.

GCF(54999,55005) = 3
LCM(54999,55005) = ( 54999 × 55005) / 3
LCM(54999,55005) = 3025219995 / 3
LCM(54999,55005) = 1008406665

Least Common Multiple (LCM) of 54999 and 55005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54999 and 55005. First we will calculate the prime factors of 54999 and 55005.

Prime Factorization of 54999

Prime factors of 54999 are 3, 7, 97. Prime factorization of 54999 in exponential form is:

54999 = 34 × 71 × 971

Prime Factorization of 55005

Prime factors of 55005 are 3, 5, 19, 193. Prime factorization of 55005 in exponential form is:

55005 = 31 × 51 × 191 × 1931

Now multiplying the highest exponent prime factors to calculate the LCM of 54999 and 55005.

LCM(54999,55005) = 34 × 71 × 971 × 51 × 191 × 1931
LCM(54999,55005) = 1008406665