What is the Least Common Multiple of 43152 and 43170?

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 43152 and 43170 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43152 and 43170, than apply into the LCM equation.

GCF(43152,43170) = 6
LCM(43152,43170) = ( 43152 × 43170) / 6
LCM(43152,43170) = 1862871840 / 6
LCM(43152,43170) = 310478640

Least Common Multiple (LCM) of 43152 and 43170 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43152 and 43170. First we will calculate the prime factors of 43152 and 43170.

Prime Factorization of 43152

Prime Factorization of 43170

Now multiplying the highest exponent prime factors to calculate the LCM of 43152 and 43170.

LCM(43152,43170) = 2⁴ × 3¹ × 29¹ × 31¹ × 5¹ × 1439¹
LCM(43152,43170) = 310478640