What is the Least Common Multiple of 32160 and 32178?

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 32160 and 32178 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32160 and 32178, than apply into the LCM equation.

GCF(32160,32178) = 6
LCM(32160,32178) = ( 32160 × 32178) / 6
LCM(32160,32178) = 1034844480 / 6
LCM(32160,32178) = 172474080

Least Common Multiple (LCM) of 32160 and 32178 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32160 and 32178. First we will calculate the prime factors of 32160 and 32178.

Prime Factorization of 32160

Prime Factorization of 32178

Now multiplying the highest exponent prime factors to calculate the LCM of 32160 and 32178.

LCM(32160,32178) = 2⁵ × 3¹ × 5¹ × 67¹ × 31¹ × 173¹
LCM(32160,32178) = 172474080