What is the Least Common Multiple of 1978 and 1984?

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 1978 and 1984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1978 and 1984, than apply into the LCM equation.

GCF(1978,1984) = 2
LCM(1978,1984) = ( 1978 × 1984) / 2
LCM(1978,1984) = 3924352 / 2
LCM(1978,1984) = 1962176

Least Common Multiple (LCM) of 1978 and 1984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1978 and 1984. First we will calculate the prime factors of 1978 and 1984.

Prime Factorization of 1978

Prime Factorization of 1984

Now multiplying the highest exponent prime factors to calculate the LCM of 1978 and 1984.

LCM(1978,1984) = 2⁶ × 23¹ × 43¹ × 31¹
LCM(1978,1984) = 1962176