What is the Least Common Multiple of 13770 and 13785?

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 13770 and 13785 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13770 and 13785, than apply into the LCM equation.

GCF(13770,13785) = 15
LCM(13770,13785) = ( 13770 × 13785) / 15
LCM(13770,13785) = 189819450 / 15
LCM(13770,13785) = 12654630

Least Common Multiple (LCM) of 13770 and 13785 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13770 and 13785. First we will calculate the prime factors of 13770 and 13785.

Prime Factorization of 13770

Prime Factorization of 13785

Now multiplying the highest exponent prime factors to calculate the LCM of 13770 and 13785.

LCM(13770,13785) = 2¹ × 3⁴ × 5¹ × 17¹ × 919¹
LCM(13770,13785) = 12654630