What is the Least Common Multiple of 1905 and 1924?

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 1905 and 1924 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1905 and 1924, than apply into the LCM equation.

GCF(1905,1924) = 1
LCM(1905,1924) = ( 1905 × 1924) / 1
LCM(1905,1924) = 3665220 / 1
LCM(1905,1924) = 3665220

Least Common Multiple (LCM) of 1905 and 1924 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1905 and 1924. First we will calculate the prime factors of 1905 and 1924.

Prime Factorization of 1905

Prime Factorization of 1924

Now multiplying the highest exponent prime factors to calculate the LCM of 1905 and 1924.

LCM(1905,1924) = 3¹ × 5¹ × 127¹ × 2² × 13¹ × 37¹
LCM(1905,1924) = 3665220