What is the Least Common Multiple of 34638 and 34656?

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 34638 and 34656 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34638 and 34656, than apply into the LCM equation.

GCF(34638,34656) = 6
LCM(34638,34656) = ( 34638 × 34656) / 6
LCM(34638,34656) = 1200414528 / 6
LCM(34638,34656) = 200069088

Least Common Multiple (LCM) of 34638 and 34656 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34638 and 34656. First we will calculate the prime factors of 34638 and 34656.

Prime Factorization of 34638

Prime Factorization of 34656

Now multiplying the highest exponent prime factors to calculate the LCM of 34638 and 34656.

LCM(34638,34656) = 2⁵ × 3¹ × 23¹ × 251¹ × 19²
LCM(34638,34656) = 200069088