What is the Least Common Multiple of 1524 and 1536?

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 1524 and 1536 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1524 and 1536, than apply into the LCM equation.

GCF(1524,1536) = 12
LCM(1524,1536) = ( 1524 × 1536) / 12
LCM(1524,1536) = 2340864 / 12
LCM(1524,1536) = 195072

Least Common Multiple (LCM) of 1524 and 1536 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1524 and 1536. First we will calculate the prime factors of 1524 and 1536.

Prime Factorization of 1524

Prime Factorization of 1536

Now multiplying the highest exponent prime factors to calculate the LCM of 1524 and 1536.

LCM(1524,1536) = 2⁹ × 3¹ × 127¹
LCM(1524,1536) = 195072