What is the Least Common Multiple of 2014 and 2033?

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 2014 and 2033 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2014 and 2033, than apply into the LCM equation.

GCF(2014,2033) = 19
LCM(2014,2033) = ( 2014 × 2033) / 19
LCM(2014,2033) = 4094462 / 19
LCM(2014,2033) = 215498

Least Common Multiple (LCM) of 2014 and 2033 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2014 and 2033. First we will calculate the prime factors of 2014 and 2033.

Prime Factorization of 2014

Prime Factorization of 2033

Now multiplying the highest exponent prime factors to calculate the LCM of 2014 and 2033.

LCM(2014,2033) = 2¹ × 19¹ × 53¹ × 107¹
LCM(2014,2033) = 215498