What is the Least Common Multiple of 85749 and 85755?

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 of 85749 and 85755 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85749 and 85755, than apply into the LCM equation.

GCF(85749,85755) = 3
LCM(85749,85755) = ( 85749 × 85755) / 3
LCM(85749,85755) = 7353405495 / 3
LCM(85749,85755) = 2451135165

Least Common Multiple (LCM) of 85749 and 85755 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85749 and 85755. First we will calculate the prime factors of 85749 and 85755.

Prime Factorization of 85749

Prime Factorization of 85755

Now multiplying the highest exponent prime factors to calculate the LCM of 85749 and 85755.

LCM(85749,85755) = 3¹ × 101¹ × 283¹ × 5¹ × 5717¹
LCM(85749,85755) = 2451135165