What is the Least Common Multiple of 1972 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 1972 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 1972 and 1984, than apply into the LCM equation.

GCF(1972,1984) = 4
LCM(1972,1984) = ( 1972 × 1984) / 4
LCM(1972,1984) = 3912448 / 4
LCM(1972,1984) = 978112

Least Common Multiple (LCM) of 1972 and 1984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1972 and 1984. First we will calculate the prime factors of 1972 and 1984.

Prime Factorization of 1972

Prime Factorization of 1984

Now multiplying the highest exponent prime factors to calculate the LCM of 1972 and 1984.

LCM(1972,1984) = 2⁶ × 17¹ × 29¹ × 31¹
LCM(1972,1984) = 978112