What is the Least Common Multiple of 34719 and 34728?

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 34719 and 34728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34719 and 34728, than apply into the LCM equation.

GCF(34719,34728) = 3
LCM(34719,34728) = ( 34719 × 34728) / 3
LCM(34719,34728) = 1205721432 / 3
LCM(34719,34728) = 401907144

Least Common Multiple (LCM) of 34719 and 34728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34719 and 34728. First we will calculate the prime factors of 34719 and 34728.

Prime Factorization of 34719

Prime Factorization of 34728

Now multiplying the highest exponent prime factors to calculate the LCM of 34719 and 34728.

LCM(34719,34728) = 3¹ × 71¹ × 163¹ × 2³ × 1447¹
LCM(34719,34728) = 401907144