What is the Least Common Multiple of 1600 and 1619?

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 1600 and 1619 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1600 and 1619, than apply into the LCM equation.

GCF(1600,1619) = 1
LCM(1600,1619) = ( 1600 × 1619) / 1
LCM(1600,1619) = 2590400 / 1
LCM(1600,1619) = 2590400

Least Common Multiple (LCM) of 1600 and 1619 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1600 and 1619. First we will calculate the prime factors of 1600 and 1619.

Prime Factorization of 1600

Prime Factorization of 1619

Now multiplying the highest exponent prime factors to calculate the LCM of 1600 and 1619.

LCM(1600,1619) = 2⁶ × 5² × 1619¹
LCM(1600,1619) = 2590400