What is the Least Common Multiple of 33744 and 33762?

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 33744 and 33762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33744 and 33762, than apply into the LCM equation.

GCF(33744,33762) = 6
LCM(33744,33762) = ( 33744 × 33762) / 6
LCM(33744,33762) = 1139264928 / 6
LCM(33744,33762) = 189877488

Least Common Multiple (LCM) of 33744 and 33762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33744 and 33762. First we will calculate the prime factors of 33744 and 33762.

Prime Factorization of 33744

Prime Factorization of 33762

Now multiplying the highest exponent prime factors to calculate the LCM of 33744 and 33762.

LCM(33744,33762) = 2⁴ × 3¹ × 19¹ × 37¹ × 17¹ × 331¹
LCM(33744,33762) = 189877488