What is the Least Common Multiple of 19600 and 19617?

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 19600 and 19617 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19600 and 19617, than apply into the LCM equation.

GCF(19600,19617) = 1
LCM(19600,19617) = ( 19600 × 19617) / 1
LCM(19600,19617) = 384493200 / 1
LCM(19600,19617) = 384493200

Least Common Multiple (LCM) of 19600 and 19617 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19600 and 19617. First we will calculate the prime factors of 19600 and 19617.

Prime Factorization of 19600

Prime Factorization of 19617

Now multiplying the highest exponent prime factors to calculate the LCM of 19600 and 19617.

LCM(19600,19617) = 2⁴ × 5² × 7² × 3¹ × 13¹ × 503¹
LCM(19600,19617) = 384493200