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What is the Least Common Multiple of 40791 and 40800?

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 40791 and 40800 is 554757600.

LCM(40791,40800) = 554757600

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Least Common Multiple of 40791 and 40800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40791 and 40800, than apply into the LCM equation.

GCF(40791,40800) = 3
LCM(40791,40800) = ( 40791 × 40800) / 3
LCM(40791,40800) = 1664272800 / 3
LCM(40791,40800) = 554757600

Least Common Multiple (LCM) of 40791 and 40800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40791 and 40800. First we will calculate the prime factors of 40791 and 40800.

Prime Factorization of 40791

Prime factors of 40791 are 3, 13597. Prime factorization of 40791 in exponential form is:

40791 = 31 × 135971

Prime Factorization of 40800

Prime factors of 40800 are 2, 3, 5, 17. Prime factorization of 40800 in exponential form is:

40800 = 25 × 31 × 52 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 40791 and 40800.

LCM(40791,40800) = 31 × 135971 × 25 × 52 × 171
LCM(40791,40800) = 554757600