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What is the Least Common Multiple of 65394 and 65400?

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 65394 and 65400 is 712794600.

LCM(65394,65400) = 712794600

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Least Common Multiple of 65394 and 65400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65394 and 65400, than apply into the LCM equation.

GCF(65394,65400) = 6
LCM(65394,65400) = ( 65394 × 65400) / 6
LCM(65394,65400) = 4276767600 / 6
LCM(65394,65400) = 712794600

Least Common Multiple (LCM) of 65394 and 65400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65394 and 65400. First we will calculate the prime factors of 65394 and 65400.

Prime Factorization of 65394

Prime factors of 65394 are 2, 3, 7, 173. Prime factorization of 65394 in exponential form is:

65394 = 21 × 33 × 71 × 1731

Prime Factorization of 65400

Prime factors of 65400 are 2, 3, 5, 109. Prime factorization of 65400 in exponential form is:

65400 = 23 × 31 × 52 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 65394 and 65400.

LCM(65394,65400) = 23 × 33 × 71 × 1731 × 52 × 1091
LCM(65394,65400) = 712794600