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What is the Least Common Multiple of 85 and 105?

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 105 is 1785.

LCM(85,105) = 1785

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Least Common Multiple of 85 and 105 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 105, than apply into the LCM equation.

GCF(85,105) = 5
LCM(85,105) = ( 85 × 105) / 5
LCM(85,105) = 8925 / 5
LCM(85,105) = 1785

Least Common Multiple (LCM) of 85 and 105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85 and 105. First we will calculate the prime factors of 85 and 105.

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 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 31 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 85 and 105.

LCM(85,105) = 51 × 171 × 31 × 71
LCM(85,105) = 1785

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