What is the Least Common Multiple of 2030 and 2048?

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 2048 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 2048, than apply into the LCM equation.

GCF(2030,2048) = 2
LCM(2030,2048) = ( 2030 × 2048) / 2
LCM(2030,2048) = 4157440 / 2
LCM(2030,2048) = 2078720

Least Common Multiple (LCM) of 2030 and 2048 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2030 and 2048. First we will calculate the prime factors of 2030 and 2048.

Prime Factorization of 2030

Prime Factorization of 2048

Now multiplying the highest exponent prime factors to calculate the LCM of 2030 and 2048.

LCM(2030,2048) = 2¹¹ × 5¹ × 7¹ × 29¹
LCM(2030,2048) = 2078720