What is the Least Common Multiple of 69144 and 69152?

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 69144 and 69152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69144 and 69152, than apply into the LCM equation.

GCF(69144,69152) = 8
LCM(69144,69152) = ( 69144 × 69152) / 8
LCM(69144,69152) = 4781445888 / 8
LCM(69144,69152) = 597680736

Least Common Multiple (LCM) of 69144 and 69152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69144 and 69152. First we will calculate the prime factors of 69144 and 69152.

Prime Factorization of 69144

Prime Factorization of 69152

Now multiplying the highest exponent prime factors to calculate the LCM of 69144 and 69152.

LCM(69144,69152) = 2⁵ × 3¹ × 43¹ × 67¹ × 2161¹
LCM(69144,69152) = 597680736