What is the Least Common Multiple of 37638 and 37648?

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 37638 and 37648 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37638 and 37648, than apply into the LCM equation.

GCF(37638,37648) = 2
LCM(37638,37648) = ( 37638 × 37648) / 2
LCM(37638,37648) = 1416995424 / 2
LCM(37638,37648) = 708497712

Least Common Multiple (LCM) of 37638 and 37648 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37638 and 37648. First we will calculate the prime factors of 37638 and 37648.

Prime Factorization of 37638

Prime Factorization of 37648

Now multiplying the highest exponent prime factors to calculate the LCM of 37638 and 37648.

LCM(37638,37648) = 2⁴ × 3³ × 17¹ × 41¹ × 13¹ × 181¹
LCM(37638,37648) = 708497712