What is the Least Common Multiple of 67680 and 67696?

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 67696 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 67696, than apply into the LCM equation.

GCF(67680,67696) = 16
LCM(67680,67696) = ( 67680 × 67696) / 16
LCM(67680,67696) = 4581665280 / 16
LCM(67680,67696) = 286354080

Least Common Multiple (LCM) of 67680 and 67696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67680 and 67696. First we will calculate the prime factors of 67680 and 67696.

Prime Factorization of 67680

Prime Factorization of 67696

Now multiplying the highest exponent prime factors to calculate the LCM of 67680 and 67696.

LCM(67680,67696) = 2⁵ × 3² × 5¹ × 47¹ × 4231¹
LCM(67680,67696) = 286354080