What is the Least Common Multiple of 13650 and 13670?

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 13650 and 13670 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13650 and 13670, than apply into the LCM equation.

GCF(13650,13670) = 10
LCM(13650,13670) = ( 13650 × 13670) / 10
LCM(13650,13670) = 186595500 / 10
LCM(13650,13670) = 18659550

Least Common Multiple (LCM) of 13650 and 13670 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13650 and 13670. First we will calculate the prime factors of 13650 and 13670.

Prime Factorization of 13650

Prime Factorization of 13670

Now multiplying the highest exponent prime factors to calculate the LCM of 13650 and 13670.

LCM(13650,13670) = 2¹ × 3¹ × 5² × 7¹ × 13¹ × 1367¹
LCM(13650,13670) = 18659550