What is the Least Common Multiple of 3450 and 3465?

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 3450 and 3465 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3450 and 3465, than apply into the LCM equation.

GCF(3450,3465) = 15
LCM(3450,3465) = ( 3450 × 3465) / 15
LCM(3450,3465) = 11954250 / 15
LCM(3450,3465) = 796950

Least Common Multiple (LCM) of 3450 and 3465 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3450 and 3465. First we will calculate the prime factors of 3450 and 3465.

Prime Factorization of 3450

Prime Factorization of 3465

Now multiplying the highest exponent prime factors to calculate the LCM of 3450 and 3465.

LCM(3450,3465) = 2¹ × 3² × 5² × 23¹ × 7¹ × 11¹
LCM(3450,3465) = 796950