What is the Least Common Multiple of 3210 and 3225?

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 3210 and 3225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3210 and 3225, than apply into the LCM equation.

GCF(3210,3225) = 15
LCM(3210,3225) = ( 3210 × 3225) / 15
LCM(3210,3225) = 10352250 / 15
LCM(3210,3225) = 690150

Least Common Multiple (LCM) of 3210 and 3225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3210 and 3225. First we will calculate the prime factors of 3210 and 3225.

Prime Factorization of 3210

Prime Factorization of 3225

Now multiplying the highest exponent prime factors to calculate the LCM of 3210 and 3225.

LCM(3210,3225) = 2¹ × 3¹ × 5² × 107¹ × 43¹
LCM(3210,3225) = 690150