What is the Least Common Multiple of 1900 and 1918?

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 1900 and 1918 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1900 and 1918, than apply into the LCM equation.

GCF(1900,1918) = 2
LCM(1900,1918) = ( 1900 × 1918) / 2
LCM(1900,1918) = 3644200 / 2
LCM(1900,1918) = 1822100

Least Common Multiple (LCM) of 1900 and 1918 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1900 and 1918. First we will calculate the prime factors of 1900 and 1918.

Prime Factorization of 1900

Prime Factorization of 1918

Now multiplying the highest exponent prime factors to calculate the LCM of 1900 and 1918.

LCM(1900,1918) = 2² × 5² × 19¹ × 7¹ × 137¹
LCM(1900,1918) = 1822100