What is the Least Common Multiple of 67752 and 67760?

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 67752 and 67760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67752 and 67760, than apply into the LCM equation.

GCF(67752,67760) = 8
LCM(67752,67760) = ( 67752 × 67760) / 8
LCM(67752,67760) = 4590875520 / 8
LCM(67752,67760) = 573859440

Least Common Multiple (LCM) of 67752 and 67760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67752 and 67760. First we will calculate the prime factors of 67752 and 67760.

Prime Factorization of 67752

Prime Factorization of 67760

Now multiplying the highest exponent prime factors to calculate the LCM of 67752 and 67760.

LCM(67752,67760) = 2⁴ × 3² × 941¹ × 5¹ × 7¹ × 11²
LCM(67752,67760) = 573859440