What is the Least Common Multiple of 21714 and 21728?

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 21714 and 21728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21714 and 21728, than apply into the LCM equation.

GCF(21714,21728) = 14
LCM(21714,21728) = ( 21714 × 21728) / 14
LCM(21714,21728) = 471801792 / 14
LCM(21714,21728) = 33700128

Least Common Multiple (LCM) of 21714 and 21728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21714 and 21728. First we will calculate the prime factors of 21714 and 21728.

Prime Factorization of 21714

Prime Factorization of 21728

Now multiplying the highest exponent prime factors to calculate the LCM of 21714 and 21728.

LCM(21714,21728) = 2⁵ × 3¹ × 7¹ × 11¹ × 47¹ × 97¹
LCM(21714,21728) = 33700128