What is the Least Common Multiple of 1880 and 1900?

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 1880 and 1900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1880 and 1900, than apply into the LCM equation.

GCF(1880,1900) = 20
LCM(1880,1900) = ( 1880 × 1900) / 20
LCM(1880,1900) = 3572000 / 20
LCM(1880,1900) = 178600

Least Common Multiple (LCM) of 1880 and 1900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1880 and 1900. First we will calculate the prime factors of 1880 and 1900.

Prime Factorization of 1880

Prime Factorization of 1900

Now multiplying the highest exponent prime factors to calculate the LCM of 1880 and 1900.

LCM(1880,1900) = 2³ × 5² × 47¹ × 19¹
LCM(1880,1900) = 178600