What is the Least Common Multiple of 1974 and 1994?

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 1974 and 1994 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1974 and 1994, than apply into the LCM equation.

GCF(1974,1994) = 2
LCM(1974,1994) = ( 1974 × 1994) / 2
LCM(1974,1994) = 3936156 / 2
LCM(1974,1994) = 1968078

Least Common Multiple (LCM) of 1974 and 1994 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1974 and 1994. First we will calculate the prime factors of 1974 and 1994.

Prime Factorization of 1974

Prime Factorization of 1994

Now multiplying the highest exponent prime factors to calculate the LCM of 1974 and 1994.

LCM(1974,1994) = 2¹ × 3¹ × 7¹ × 47¹ × 997¹
LCM(1974,1994) = 1968078