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What is the Least Common Multiple of 84 and 100?

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 100 is 2100.

LCM(84,100) = 2100

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Least Common Multiple of 84 and 100 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 100, than apply into the LCM equation.

GCF(84,100) = 4
LCM(84,100) = ( 84 × 100) / 4
LCM(84,100) = 8400 / 4
LCM(84,100) = 2100

Least Common Multiple (LCM) of 84 and 100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 100. First we will calculate the prime factors of 84 and 100.

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 100

Prime factors of 100 are 2, 5. Prime factorization of 100 in exponential form is:

100 = 22 × 52

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 100.

LCM(84,100) = 22 × 31 × 71 × 52
LCM(84,100) = 2100

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