What is the Least Common Multiple of 2010 and 2030?

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 2010 and 2030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2010 and 2030, than apply into the LCM equation.

GCF(2010,2030) = 10
LCM(2010,2030) = ( 2010 × 2030) / 10
LCM(2010,2030) = 4080300 / 10
LCM(2010,2030) = 408030

Least Common Multiple (LCM) of 2010 and 2030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2010 and 2030. First we will calculate the prime factors of 2010 and 2030.

Prime Factorization of 2010

Prime Factorization of 2030

Now multiplying the highest exponent prime factors to calculate the LCM of 2010 and 2030.

LCM(2010,2030) = 2¹ × 3¹ × 5¹ × 67¹ × 7¹ × 29¹
LCM(2010,2030) = 408030