What is the Least Common Multiple of 21225 and 21240?

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 21225 and 21240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21225 and 21240, than apply into the LCM equation.

GCF(21225,21240) = 15
LCM(21225,21240) = ( 21225 × 21240) / 15
LCM(21225,21240) = 450819000 / 15
LCM(21225,21240) = 30054600

Least Common Multiple (LCM) of 21225 and 21240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21225 and 21240. First we will calculate the prime factors of 21225 and 21240.

Prime Factorization of 21225

Prime Factorization of 21240

Now multiplying the highest exponent prime factors to calculate the LCM of 21225 and 21240.

LCM(21225,21240) = 3² × 5² × 283¹ × 2³ × 59¹
LCM(21225,21240) = 30054600