What is the Least Common Multiple of 1536 and 1542?

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 1542 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 1542, than apply into the LCM equation.

GCF(1536,1542) = 6
LCM(1536,1542) = ( 1536 × 1542) / 6
LCM(1536,1542) = 2368512 / 6
LCM(1536,1542) = 394752

Least Common Multiple (LCM) of 1536 and 1542 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1536 and 1542. First we will calculate the prime factors of 1536 and 1542.

Prime Factorization of 1536

Prime Factorization of 1542

Now multiplying the highest exponent prime factors to calculate the LCM of 1536 and 1542.

LCM(1536,1542) = 2⁹ × 3¹ × 257¹
LCM(1536,1542) = 394752