What is the Least Common Multiple of 1536 and 1546?

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 1536 and 1546 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1536 and 1546, than apply into the LCM equation.

GCF(1536,1546) = 2
LCM(1536,1546) = ( 1536 × 1546) / 2
LCM(1536,1546) = 2374656 / 2
LCM(1536,1546) = 1187328

Least Common Multiple (LCM) of 1536 and 1546 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1536 and 1546. First we will calculate the prime factors of 1536 and 1546.

Prime Factorization of 1536

Prime Factorization of 1546

Now multiplying the highest exponent prime factors to calculate the LCM of 1536 and 1546.

LCM(1536,1546) = 2⁹ × 3¹ × 773¹
LCM(1536,1546) = 1187328