What is the Least Common Multiple of 21728 and 21742?

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 21728 and 21742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21728 and 21742, than apply into the LCM equation.

GCF(21728,21742) = 14
LCM(21728,21742) = ( 21728 × 21742) / 14
LCM(21728,21742) = 472410176 / 14
LCM(21728,21742) = 33743584

Least Common Multiple (LCM) of 21728 and 21742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21728 and 21742. First we will calculate the prime factors of 21728 and 21742.

Prime Factorization of 21728

Prime Factorization of 21742

Now multiplying the highest exponent prime factors to calculate the LCM of 21728 and 21742.

LCM(21728,21742) = 2⁵ × 7¹ × 97¹ × 1553¹
LCM(21728,21742) = 33743584