What is the Least Common Multiple of 1975 and 1980?

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 1975 and 1980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1975 and 1980, than apply into the LCM equation.

GCF(1975,1980) = 5
LCM(1975,1980) = ( 1975 × 1980) / 5
LCM(1975,1980) = 3910500 / 5
LCM(1975,1980) = 782100

Least Common Multiple (LCM) of 1975 and 1980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1975 and 1980. First we will calculate the prime factors of 1975 and 1980.

Prime Factorization of 1975

Prime Factorization of 1980

Now multiplying the highest exponent prime factors to calculate the LCM of 1975 and 1980.

LCM(1975,1980) = 5² × 79¹ × 2² × 3² × 11¹
LCM(1975,1980) = 782100