What is the Least Common Multiple of 1974 and 1989?

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 1989 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 1989, than apply into the LCM equation.

GCF(1974,1989) = 3
LCM(1974,1989) = ( 1974 × 1989) / 3
LCM(1974,1989) = 3926286 / 3
LCM(1974,1989) = 1308762

Least Common Multiple (LCM) of 1974 and 1989 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1974 and 1989. First we will calculate the prime factors of 1974 and 1989.

Prime Factorization of 1974

Prime Factorization of 1989

Now multiplying the highest exponent prime factors to calculate the LCM of 1974 and 1989.

LCM(1974,1989) = 2¹ × 3² × 7¹ × 47¹ × 13¹ × 17¹
LCM(1974,1989) = 1308762