What is the Least Common Multiple of 21750 and 21760?

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 21750 and 21760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21750 and 21760, than apply into the LCM equation.

GCF(21750,21760) = 10
LCM(21750,21760) = ( 21750 × 21760) / 10
LCM(21750,21760) = 473280000 / 10
LCM(21750,21760) = 47328000

Least Common Multiple (LCM) of 21750 and 21760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21750 and 21760. First we will calculate the prime factors of 21750 and 21760.

Prime Factorization of 21750

Prime Factorization of 21760

Now multiplying the highest exponent prime factors to calculate the LCM of 21750 and 21760.

LCM(21750,21760) = 2⁸ × 3¹ × 5³ × 29¹ × 17¹
LCM(21750,21760) = 47328000