What is the Least Common Multiple of 1890 and 1899?

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 1890 and 1899 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1890 and 1899, than apply into the LCM equation.

GCF(1890,1899) = 9
LCM(1890,1899) = ( 1890 × 1899) / 9
LCM(1890,1899) = 3589110 / 9
LCM(1890,1899) = 398790

Least Common Multiple (LCM) of 1890 and 1899 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1890 and 1899. First we will calculate the prime factors of 1890 and 1899.

Prime Factorization of 1890

Prime Factorization of 1899

Now multiplying the highest exponent prime factors to calculate the LCM of 1890 and 1899.

LCM(1890,1899) = 2¹ × 3³ × 5¹ × 7¹ × 211¹
LCM(1890,1899) = 398790