What is the Least Common Multiple of 2030 and 2050?

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 2030 and 2050 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2030 and 2050, than apply into the LCM equation.

GCF(2030,2050) = 10
LCM(2030,2050) = ( 2030 × 2050) / 10
LCM(2030,2050) = 4161500 / 10
LCM(2030,2050) = 416150

Least Common Multiple (LCM) of 2030 and 2050 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2030 and 2050. First we will calculate the prime factors of 2030 and 2050.

Prime Factorization of 2030

Prime Factorization of 2050

Now multiplying the highest exponent prime factors to calculate the LCM of 2030 and 2050.

LCM(2030,2050) = 2¹ × 5² × 7¹ × 29¹ × 41¹
LCM(2030,2050) = 416150