What is the Least Common Multiple of 1968 and 1975?

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 1968 and 1975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1968 and 1975, than apply into the LCM equation.

GCF(1968,1975) = 1
LCM(1968,1975) = ( 1968 × 1975) / 1
LCM(1968,1975) = 3886800 / 1
LCM(1968,1975) = 3886800

Least Common Multiple (LCM) of 1968 and 1975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1968 and 1975. First we will calculate the prime factors of 1968 and 1975.

Prime Factorization of 1968

Prime Factorization of 1975

Now multiplying the highest exponent prime factors to calculate the LCM of 1968 and 1975.

LCM(1968,1975) = 2⁴ × 3¹ × 41¹ × 5² × 79¹
LCM(1968,1975) = 3886800