What is the Least Common Multiple of 1948 and 1965?

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 1948 and 1965 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1948 and 1965, than apply into the LCM equation.

GCF(1948,1965) = 1
LCM(1948,1965) = ( 1948 × 1965) / 1
LCM(1948,1965) = 3827820 / 1
LCM(1948,1965) = 3827820

Least Common Multiple (LCM) of 1948 and 1965 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1948 and 1965. First we will calculate the prime factors of 1948 and 1965.

Prime Factorization of 1948

Prime Factorization of 1965

Now multiplying the highest exponent prime factors to calculate the LCM of 1948 and 1965.

LCM(1948,1965) = 2² × 487¹ × 3¹ × 5¹ × 131¹
LCM(1948,1965) = 3827820