What is the Least Common Multiple of 21114 and 21128?

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 21114 and 21128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21114 and 21128, than apply into the LCM equation.

GCF(21114,21128) = 2
LCM(21114,21128) = ( 21114 × 21128) / 2
LCM(21114,21128) = 446096592 / 2
LCM(21114,21128) = 223048296

Least Common Multiple (LCM) of 21114 and 21128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21114 and 21128. First we will calculate the prime factors of 21114 and 21128.

Prime Factorization of 21114

Prime Factorization of 21128

Now multiplying the highest exponent prime factors to calculate the LCM of 21114 and 21128.

LCM(21114,21128) = 2³ × 3³ × 17¹ × 23¹ × 19¹ × 139¹
LCM(21114,21128) = 223048296