What is the Least Common Multiple of 1938 and 1954?

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 1938 and 1954 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1938 and 1954, than apply into the LCM equation.

GCF(1938,1954) = 2
LCM(1938,1954) = ( 1938 × 1954) / 2
LCM(1938,1954) = 3786852 / 2
LCM(1938,1954) = 1893426

Least Common Multiple (LCM) of 1938 and 1954 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1938 and 1954. First we will calculate the prime factors of 1938 and 1954.

Prime Factorization of 1938

Prime Factorization of 1954

Now multiplying the highest exponent prime factors to calculate the LCM of 1938 and 1954.

LCM(1938,1954) = 2¹ × 3¹ × 17¹ × 19¹ × 977¹
LCM(1938,1954) = 1893426