What is the Least Common Multiple of 78144 and 78156?

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 78144 and 78156 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78144 and 78156, than apply into the LCM equation.

GCF(78144,78156) = 12
LCM(78144,78156) = ( 78144 × 78156) / 12
LCM(78144,78156) = 6107422464 / 12
LCM(78144,78156) = 508951872

Least Common Multiple (LCM) of 78144 and 78156 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78144 and 78156. First we will calculate the prime factors of 78144 and 78156.

Prime Factorization of 78144

Prime Factorization of 78156

Now multiplying the highest exponent prime factors to calculate the LCM of 78144 and 78156.

LCM(78144,78156) = 2⁶ × 3² × 11¹ × 37¹ × 13¹ × 167¹
LCM(78144,78156) = 508951872