What is the Least Common Multiple of 1972 and 1985?

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 1985 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 1985, than apply into the LCM equation.

GCF(1972,1985) = 1
LCM(1972,1985) = ( 1972 × 1985) / 1
LCM(1972,1985) = 3914420 / 1
LCM(1972,1985) = 3914420

Least Common Multiple (LCM) of 1972 and 1985 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1972 and 1985. First we will calculate the prime factors of 1972 and 1985.

Prime Factorization of 1972

Prime Factorization of 1985

Now multiplying the highest exponent prime factors to calculate the LCM of 1972 and 1985.

LCM(1972,1985) = 2² × 17¹ × 29¹ × 5¹ × 397¹
LCM(1972,1985) = 3914420