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What is the Least Common Multiple of 85 and 104?

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 85 and 104 is 8840.

LCM(85,104) = 8840

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Least Common Multiple of 85 and 104 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85 and 104, than apply into the LCM equation.

GCF(85,104) = 1
LCM(85,104) = ( 85 × 104) / 1
LCM(85,104) = 8840 / 1
LCM(85,104) = 8840

Least Common Multiple (LCM) of 85 and 104 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85 and 104. First we will calculate the prime factors of 85 and 104.

Prime Factorization of 85

Prime factors of 85 are 5, 17. Prime factorization of 85 in exponential form is:

85 = 51 × 171

Prime Factorization of 104

Prime factors of 104 are 2, 13. Prime factorization of 104 in exponential form is:

104 = 23 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 85 and 104.

LCM(85,104) = 51 × 171 × 23 × 131
LCM(85,104) = 8840

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