What is the Least Common Multiple of 1896 and 1905?

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 1896 and 1905 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1896 and 1905, than apply into the LCM equation.

GCF(1896,1905) = 3
LCM(1896,1905) = ( 1896 × 1905) / 3
LCM(1896,1905) = 3611880 / 3
LCM(1896,1905) = 1203960

Least Common Multiple (LCM) of 1896 and 1905 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1896 and 1905. First we will calculate the prime factors of 1896 and 1905.

Prime Factorization of 1896

Prime Factorization of 1905

Now multiplying the highest exponent prime factors to calculate the LCM of 1896 and 1905.

LCM(1896,1905) = 2³ × 3¹ × 79¹ × 5¹ × 127¹
LCM(1896,1905) = 1203960