What is the Least Common Multiple of 1870 and 1890?

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 1870 and 1890 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1870 and 1890, than apply into the LCM equation.

GCF(1870,1890) = 10
LCM(1870,1890) = ( 1870 × 1890) / 10
LCM(1870,1890) = 3534300 / 10
LCM(1870,1890) = 353430

Least Common Multiple (LCM) of 1870 and 1890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1870 and 1890. First we will calculate the prime factors of 1870 and 1890.

Prime Factorization of 1870

Prime Factorization of 1890

Now multiplying the highest exponent prime factors to calculate the LCM of 1870 and 1890.

LCM(1870,1890) = 2¹ × 5¹ × 11¹ × 17¹ × 3³ × 7¹
LCM(1870,1890) = 353430