What is the Least Common Multiple of 38760 and 38780?

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 38760 and 38780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38760 and 38780, than apply into the LCM equation.

GCF(38760,38780) = 20
LCM(38760,38780) = ( 38760 × 38780) / 20
LCM(38760,38780) = 1503112800 / 20
LCM(38760,38780) = 75155640

Least Common Multiple (LCM) of 38760 and 38780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38760 and 38780. First we will calculate the prime factors of 38760 and 38780.

Prime Factorization of 38760

Prime Factorization of 38780

Now multiplying the highest exponent prime factors to calculate the LCM of 38760 and 38780.

LCM(38760,38780) = 2³ × 3¹ × 5¹ × 17¹ × 19¹ × 7¹ × 277¹
LCM(38760,38780) = 75155640