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What is the Least Common Multiple of 84 and 93?

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 84 and 93 is 2604.

LCM(84,93) = 2604

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Least Common Multiple of 84 and 93 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 93, than apply into the LCM equation.

GCF(84,93) = 3
LCM(84,93) = ( 84 × 93) / 3
LCM(84,93) = 7812 / 3
LCM(84,93) = 2604

Least Common Multiple (LCM) of 84 and 93 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 93. First we will calculate the prime factors of 84 and 93.

Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 22 × 31 × 71

Prime Factorization of 93

Prime factors of 93 are 3, 31. Prime factorization of 93 in exponential form is:

93 = 31 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 93.

LCM(84,93) = 22 × 31 × 71 × 311
LCM(84,93) = 2604

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