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What is the Least Common Multiple of 84 and 90?

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 90 is 1260.

LCM(84,90) = 1260

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Least Common Multiple of 84 and 90 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 90, than apply into the LCM equation.

GCF(84,90) = 6
LCM(84,90) = ( 84 × 90) / 6
LCM(84,90) = 7560 / 6
LCM(84,90) = 1260

Least Common Multiple (LCM) of 84 and 90 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 90. First we will calculate the prime factors of 84 and 90.

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 90

Prime factors of 90 are 2, 3, 5. Prime factorization of 90 in exponential form is:

90 = 21 × 32 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 90.

LCM(84,90) = 22 × 32 × 71 × 51
LCM(84,90) = 1260

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