What is the Least Common Multiple of 1954 and 1971?

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 1954 and 1971 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1954 and 1971, than apply into the LCM equation.

GCF(1954,1971) = 1
LCM(1954,1971) = ( 1954 × 1971) / 1
LCM(1954,1971) = 3851334 / 1
LCM(1954,1971) = 3851334

Least Common Multiple (LCM) of 1954 and 1971 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1954 and 1971. First we will calculate the prime factors of 1954 and 1971.

Prime Factorization of 1954

Prime Factorization of 1971

Now multiplying the highest exponent prime factors to calculate the LCM of 1954 and 1971.

LCM(1954,1971) = 2¹ × 977¹ × 3³ × 73¹
LCM(1954,1971) = 3851334