What is the Least Common Multiple of 67680 and 67700?

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 67680 and 67700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67680 and 67700, than apply into the LCM equation.

GCF(67680,67700) = 20
LCM(67680,67700) = ( 67680 × 67700) / 20
LCM(67680,67700) = 4581936000 / 20
LCM(67680,67700) = 229096800

Least Common Multiple (LCM) of 67680 and 67700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67680 and 67700. First we will calculate the prime factors of 67680 and 67700.

Prime Factorization of 67680

Prime Factorization of 67700

Now multiplying the highest exponent prime factors to calculate the LCM of 67680 and 67700.

LCM(67680,67700) = 2⁵ × 3² × 5² × 47¹ × 677¹
LCM(67680,67700) = 229096800