What is the Least Common Multiple of 67872 and 67888?

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 67872 and 67888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67872 and 67888, than apply into the LCM equation.

GCF(67872,67888) = 16
LCM(67872,67888) = ( 67872 × 67888) / 16
LCM(67872,67888) = 4607694336 / 16
LCM(67872,67888) = 287980896

Least Common Multiple (LCM) of 67872 and 67888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67872 and 67888. First we will calculate the prime factors of 67872 and 67888.

Prime Factorization of 67872

Prime Factorization of 67888

Now multiplying the highest exponent prime factors to calculate the LCM of 67872 and 67888.

LCM(67872,67888) = 2⁵ × 3¹ × 7¹ × 101¹ × 4243¹
LCM(67872,67888) = 287980896