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What is the Least Common Multiple of 85722 and 85731?

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 85722 and 85731 is 2449677594.

LCM(85722,85731) = 2449677594

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Least Common Multiple of 85722 and 85731 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85722 and 85731, than apply into the LCM equation.

GCF(85722,85731) = 3
LCM(85722,85731) = ( 85722 × 85731) / 3
LCM(85722,85731) = 7349032782 / 3
LCM(85722,85731) = 2449677594

Least Common Multiple (LCM) of 85722 and 85731 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85722 and 85731. First we will calculate the prime factors of 85722 and 85731.

Prime Factorization of 85722

Prime factors of 85722 are 2, 3, 7, 13, 157. Prime factorization of 85722 in exponential form is:

85722 = 21 × 31 × 71 × 131 × 1571

Prime Factorization of 85731

Prime factors of 85731 are 3, 17, 41. Prime factorization of 85731 in exponential form is:

85731 = 31 × 171 × 412

Now multiplying the highest exponent prime factors to calculate the LCM of 85722 and 85731.

LCM(85722,85731) = 21 × 31 × 71 × 131 × 1571 × 171 × 412
LCM(85722,85731) = 2449677594