What is the Least Common Multiple of 21450 and 21465?

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 21450 and 21465 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21450 and 21465, than apply into the LCM equation.

GCF(21450,21465) = 15
LCM(21450,21465) = ( 21450 × 21465) / 15
LCM(21450,21465) = 460424250 / 15
LCM(21450,21465) = 30694950

Least Common Multiple (LCM) of 21450 and 21465 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21450 and 21465. First we will calculate the prime factors of 21450 and 21465.

Prime Factorization of 21450

Prime Factorization of 21465

Now multiplying the highest exponent prime factors to calculate the LCM of 21450 and 21465.

LCM(21450,21465) = 2¹ × 3⁴ × 5² × 11¹ × 13¹ × 53¹
LCM(21450,21465) = 30694950