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What is the Least Common Multiple of 84 and 91?

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 91 is 1092.

LCM(84,91) = 1092

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Least Common Multiple of 84 and 91 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 91, than apply into the LCM equation.

GCF(84,91) = 7
LCM(84,91) = ( 84 × 91) / 7
LCM(84,91) = 7644 / 7
LCM(84,91) = 1092

Least Common Multiple (LCM) of 84 and 91 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 91. First we will calculate the prime factors of 84 and 91.

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 91

Prime factors of 91 are 7, 13. Prime factorization of 91 in exponential form is:

91 = 71 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 91.

LCM(84,91) = 22 × 31 × 71 × 131
LCM(84,91) = 1092

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