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What is the Least Common Multiple of 54705 and 54710?

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 54705 and 54710 is 598582110.

LCM(54705,54710) = 598582110

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Least Common Multiple of 54705 and 54710 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54705 and 54710, than apply into the LCM equation.

GCF(54705,54710) = 5
LCM(54705,54710) = ( 54705 × 54710) / 5
LCM(54705,54710) = 2992910550 / 5
LCM(54705,54710) = 598582110

Least Common Multiple (LCM) of 54705 and 54710 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54705 and 54710. First we will calculate the prime factors of 54705 and 54710.

Prime Factorization of 54705

Prime factors of 54705 are 3, 5, 7, 521. Prime factorization of 54705 in exponential form is:

54705 = 31 × 51 × 71 × 5211

Prime Factorization of 54710

Prime factors of 54710 are 2, 5, 5471. Prime factorization of 54710 in exponential form is:

54710 = 21 × 51 × 54711

Now multiplying the highest exponent prime factors to calculate the LCM of 54705 and 54710.

LCM(54705,54710) = 31 × 51 × 71 × 5211 × 21 × 54711
LCM(54705,54710) = 598582110