What is the Least Common Multiple of 67872 and 67884?

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 67884 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 67884, than apply into the LCM equation.

GCF(67872,67884) = 12
LCM(67872,67884) = ( 67872 × 67884) / 12
LCM(67872,67884) = 4607422848 / 12
LCM(67872,67884) = 383951904

Least Common Multiple (LCM) of 67872 and 67884 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67872 and 67884. First we will calculate the prime factors of 67872 and 67884.

Prime Factorization of 67872

Prime Factorization of 67884

Now multiplying the highest exponent prime factors to calculate the LCM of 67872 and 67884.

LCM(67872,67884) = 2⁵ × 3¹ × 7¹ × 101¹ × 5657¹
LCM(67872,67884) = 383951904