What is the Least Common Multiple of 3465 and 3480?

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 3465 and 3480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3465 and 3480, than apply into the LCM equation.

GCF(3465,3480) = 15
LCM(3465,3480) = ( 3465 × 3480) / 15
LCM(3465,3480) = 12058200 / 15
LCM(3465,3480) = 803880

Least Common Multiple (LCM) of 3465 and 3480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3465 and 3480. First we will calculate the prime factors of 3465 and 3480.

Prime Factorization of 3465

Prime Factorization of 3480

Now multiplying the highest exponent prime factors to calculate the LCM of 3465 and 3480.

LCM(3465,3480) = 3² × 5¹ × 7¹ × 11¹ × 2³ × 29¹
LCM(3465,3480) = 803880