What is the Least Common Multiple of 3 and 112?

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 3 and 112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 112, than apply into the LCM equation.

GCF(3,112) = 1
LCM(3,112) = ( 3 × 112) / 1
LCM(3,112) = 336 / 1
LCM(3,112) = 336

Least Common Multiple (LCM) of 3 and 112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 112. First we will calculate the prime factors of 3 and 112.

Prime Factorization of 3

Prime Factorization of 112

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 112.

LCM(3,112) = 3¹ × 2⁴ × 7¹
LCM(3,112) = 336