What is the Least Common Multiple of 32160 and 32170?

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 32170 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 32170, than apply into the LCM equation.

GCF(32160,32170) = 10
LCM(32160,32170) = ( 32160 × 32170) / 10
LCM(32160,32170) = 1034587200 / 10
LCM(32160,32170) = 103458720

Least Common Multiple (LCM) of 32160 and 32170 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32160 and 32170. First we will calculate the prime factors of 32160 and 32170.

Prime Factorization of 32160

Prime Factorization of 32170

Now multiplying the highest exponent prime factors to calculate the LCM of 32160 and 32170.

LCM(32160,32170) = 2⁵ × 3¹ × 5¹ × 67¹ × 3217¹
LCM(32160,32170) = 103458720