What is the Least Common Multiple of 69600 and 69612?

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 69600 and 69612 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69600 and 69612, than apply into the LCM equation.

GCF(69600,69612) = 12
LCM(69600,69612) = ( 69600 × 69612) / 12
LCM(69600,69612) = 4844995200 / 12
LCM(69600,69612) = 403749600

Least Common Multiple (LCM) of 69600 and 69612 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69600 and 69612. First we will calculate the prime factors of 69600 and 69612.

Prime Factorization of 69600

Prime Factorization of 69612

Now multiplying the highest exponent prime factors to calculate the LCM of 69600 and 69612.

LCM(69600,69612) = 2⁵ × 3¹ × 5² × 29¹ × 5801¹
LCM(69600,69612) = 403749600