What is the Least Common Multiple of 1600 and 1614?

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 1614 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 1614, than apply into the LCM equation.

GCF(1600,1614) = 2
LCM(1600,1614) = ( 1600 × 1614) / 2
LCM(1600,1614) = 2582400 / 2
LCM(1600,1614) = 1291200

Least Common Multiple (LCM) of 1600 and 1614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1600 and 1614. First we will calculate the prime factors of 1600 and 1614.

Prime Factorization of 1600

Prime Factorization of 1614

Now multiplying the highest exponent prime factors to calculate the LCM of 1600 and 1614.

LCM(1600,1614) = 2⁶ × 5² × 3¹ × 269¹
LCM(1600,1614) = 1291200