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What is the Least Common Multiple of 84 and 99?

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 99 is 2772.

LCM(84,99) = 2772

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Least Common Multiple of 84 and 99 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 99, than apply into the LCM equation.

GCF(84,99) = 3
LCM(84,99) = ( 84 × 99) / 3
LCM(84,99) = 8316 / 3
LCM(84,99) = 2772

Least Common Multiple (LCM) of 84 and 99 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 99. First we will calculate the prime factors of 84 and 99.

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 99

Prime factors of 99 are 3, 11. Prime factorization of 99 in exponential form is:

99 = 32 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 99.

LCM(84,99) = 22 × 32 × 71 × 111
LCM(84,99) = 2772

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