What is the Least Common Multiple of 67770 and 67785?

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 67770 and 67785 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67770 and 67785, than apply into the LCM equation.

GCF(67770,67785) = 15
LCM(67770,67785) = ( 67770 × 67785) / 15
LCM(67770,67785) = 4593789450 / 15
LCM(67770,67785) = 306252630

Least Common Multiple (LCM) of 67770 and 67785 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67770 and 67785. First we will calculate the prime factors of 67770 and 67785.

Prime Factorization of 67770

Prime Factorization of 67785

Now multiplying the highest exponent prime factors to calculate the LCM of 67770 and 67785.

LCM(67770,67785) = 2¹ × 3³ × 5¹ × 251¹ × 4519¹
LCM(67770,67785) = 306252630