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What is the Least Common Multiple of 26394 and 26400?

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 26394 and 26400 is 116133600.

LCM(26394,26400) = 116133600

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Least Common Multiple of 26394 and 26400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26394 and 26400, than apply into the LCM equation.

GCF(26394,26400) = 6
LCM(26394,26400) = ( 26394 × 26400) / 6
LCM(26394,26400) = 696801600 / 6
LCM(26394,26400) = 116133600

Least Common Multiple (LCM) of 26394 and 26400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26394 and 26400. First we will calculate the prime factors of 26394 and 26400.

Prime Factorization of 26394

Prime factors of 26394 are 2, 3, 53, 83. Prime factorization of 26394 in exponential form is:

26394 = 21 × 31 × 531 × 831

Prime Factorization of 26400

Prime factors of 26400 are 2, 3, 5, 11. Prime factorization of 26400 in exponential form is:

26400 = 25 × 31 × 52 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 26394 and 26400.

LCM(26394,26400) = 25 × 31 × 531 × 831 × 52 × 111
LCM(26394,26400) = 116133600