What is the Least Common Multiple of 3456 and 3460?

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 3456 and 3460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3456 and 3460, than apply into the LCM equation.

GCF(3456,3460) = 4
LCM(3456,3460) = ( 3456 × 3460) / 4
LCM(3456,3460) = 11957760 / 4
LCM(3456,3460) = 2989440

Least Common Multiple (LCM) of 3456 and 3460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3456 and 3460. First we will calculate the prime factors of 3456 and 3460.

Prime Factorization of 3456

Prime Factorization of 3460

Now multiplying the highest exponent prime factors to calculate the LCM of 3456 and 3460.

LCM(3456,3460) = 2⁷ × 3³ × 5¹ × 173¹
LCM(3456,3460) = 2989440