What is the Least Common Multiple of 1945 and 1960?

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 1945 and 1960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1945 and 1960, than apply into the LCM equation.

GCF(1945,1960) = 5
LCM(1945,1960) = ( 1945 × 1960) / 5
LCM(1945,1960) = 3812200 / 5
LCM(1945,1960) = 762440

Least Common Multiple (LCM) of 1945 and 1960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1945 and 1960. First we will calculate the prime factors of 1945 and 1960.

Prime Factorization of 1945

Prime Factorization of 1960

Now multiplying the highest exponent prime factors to calculate the LCM of 1945 and 1960.

LCM(1945,1960) = 5¹ × 389¹ × 2³ × 7²
LCM(1945,1960) = 762440