What is the Least Common Multiple of 32140 and 32160?

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 32140 and 32160 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32140 and 32160, than apply into the LCM equation.

GCF(32140,32160) = 20
LCM(32140,32160) = ( 32140 × 32160) / 20
LCM(32140,32160) = 1033622400 / 20
LCM(32140,32160) = 51681120

Least Common Multiple (LCM) of 32140 and 32160 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32140 and 32160. First we will calculate the prime factors of 32140 and 32160.

Prime Factorization of 32140

Prime Factorization of 32160

Now multiplying the highest exponent prime factors to calculate the LCM of 32140 and 32160.

LCM(32140,32160) = 2⁵ × 5¹ × 1607¹ × 3¹ × 67¹
LCM(32140,32160) = 51681120