What is the Least Common Multiple of 38674 and 38688?

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 38674 and 38688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38674 and 38688, than apply into the LCM equation.

GCF(38674,38688) = 2
LCM(38674,38688) = ( 38674 × 38688) / 2
LCM(38674,38688) = 1496219712 / 2
LCM(38674,38688) = 748109856

Least Common Multiple (LCM) of 38674 and 38688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38674 and 38688. First we will calculate the prime factors of 38674 and 38688.

Prime Factorization of 38674

Prime Factorization of 38688

Now multiplying the highest exponent prime factors to calculate the LCM of 38674 and 38688.

LCM(38674,38688) = 2⁵ × 61¹ × 317¹ × 3¹ × 13¹ × 31¹
LCM(38674,38688) = 748109856