What is the Least Common Multiple of 1960 and 1974?

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 1960 and 1974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1960 and 1974, than apply into the LCM equation.

GCF(1960,1974) = 14
LCM(1960,1974) = ( 1960 × 1974) / 14
LCM(1960,1974) = 3869040 / 14
LCM(1960,1974) = 276360

Least Common Multiple (LCM) of 1960 and 1974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1960 and 1974. First we will calculate the prime factors of 1960 and 1974.

Prime Factorization of 1960

Prime Factorization of 1974

Now multiplying the highest exponent prime factors to calculate the LCM of 1960 and 1974.

LCM(1960,1974) = 2³ × 5¹ × 7² × 3¹ × 47¹
LCM(1960,1974) = 276360