What is the Least Common Multiple of 1974 and 1982?

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 1982 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 1982, than apply into the LCM equation.

GCF(1974,1982) = 2
LCM(1974,1982) = ( 1974 × 1982) / 2
LCM(1974,1982) = 3912468 / 2
LCM(1974,1982) = 1956234

Least Common Multiple (LCM) of 1974 and 1982 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1974 and 1982. First we will calculate the prime factors of 1974 and 1982.

Prime Factorization of 1974

Prime Factorization of 1982

Now multiplying the highest exponent prime factors to calculate the LCM of 1974 and 1982.

LCM(1974,1982) = 2¹ × 3¹ × 7¹ × 47¹ × 991¹
LCM(1974,1982) = 1956234