What is the Least Common Multiple of 21138 and 21152?

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 21138 and 21152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21138 and 21152, than apply into the LCM equation.

GCF(21138,21152) = 2
LCM(21138,21152) = ( 21138 × 21152) / 2
LCM(21138,21152) = 447110976 / 2
LCM(21138,21152) = 223555488

Least Common Multiple (LCM) of 21138 and 21152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21138 and 21152. First we will calculate the prime factors of 21138 and 21152.

Prime Factorization of 21138

Prime Factorization of 21152

Now multiplying the highest exponent prime factors to calculate the LCM of 21138 and 21152.

LCM(21138,21152) = 2⁵ × 3¹ × 13¹ × 271¹ × 661¹
LCM(21138,21152) = 223555488