What is the Least Common Multiple of 1952 and 1972?

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 1952 and 1972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1952 and 1972, than apply into the LCM equation.

GCF(1952,1972) = 4
LCM(1952,1972) = ( 1952 × 1972) / 4
LCM(1952,1972) = 3849344 / 4
LCM(1952,1972) = 962336

Least Common Multiple (LCM) of 1952 and 1972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1952 and 1972. First we will calculate the prime factors of 1952 and 1972.

Prime Factorization of 1952

Prime Factorization of 1972

Now multiplying the highest exponent prime factors to calculate the LCM of 1952 and 1972.

LCM(1952,1972) = 2⁵ × 61¹ × 17¹ × 29¹
LCM(1952,1972) = 962336