What is the Least Common Multiple of 21825 and 21840?

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 21825 and 21840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21825 and 21840, than apply into the LCM equation.

GCF(21825,21840) = 15
LCM(21825,21840) = ( 21825 × 21840) / 15
LCM(21825,21840) = 476658000 / 15
LCM(21825,21840) = 31777200

Least Common Multiple (LCM) of 21825 and 21840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21825 and 21840. First we will calculate the prime factors of 21825 and 21840.

Prime Factorization of 21825

Prime Factorization of 21840

Now multiplying the highest exponent prime factors to calculate the LCM of 21825 and 21840.

LCM(21825,21840) = 3² × 5² × 97¹ × 2⁴ × 7¹ × 13¹
LCM(21825,21840) = 31777200