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What is the Least Common Multiple of 34710 and 34720?

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 34710 and 34720 is 120513120.

LCM(34710,34720) = 120513120

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Least Common Multiple of 34710 and 34720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34710 and 34720, than apply into the LCM equation.

GCF(34710,34720) = 10
LCM(34710,34720) = ( 34710 × 34720) / 10
LCM(34710,34720) = 1205131200 / 10
LCM(34710,34720) = 120513120

Least Common Multiple (LCM) of 34710 and 34720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34710 and 34720. First we will calculate the prime factors of 34710 and 34720.

Prime Factorization of 34710

Prime factors of 34710 are 2, 3, 5, 13, 89. Prime factorization of 34710 in exponential form is:

34710 = 21 × 31 × 51 × 131 × 891

Prime Factorization of 34720

Prime factors of 34720 are 2, 5, 7, 31. Prime factorization of 34720 in exponential form is:

34720 = 25 × 51 × 71 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 34710 and 34720.

LCM(34710,34720) = 25 × 31 × 51 × 131 × 891 × 71 × 311
LCM(34710,34720) = 120513120