What is the Least Common Multiple of 3750 and 3765?

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 3750 and 3765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3750 and 3765, than apply into the LCM equation.

GCF(3750,3765) = 15
LCM(3750,3765) = ( 3750 × 3765) / 15
LCM(3750,3765) = 14118750 / 15
LCM(3750,3765) = 941250

Least Common Multiple (LCM) of 3750 and 3765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3750 and 3765. First we will calculate the prime factors of 3750 and 3765.

Prime Factorization of 3750

Prime Factorization of 3765

Now multiplying the highest exponent prime factors to calculate the LCM of 3750 and 3765.

LCM(3750,3765) = 2¹ × 3¹ × 5⁴ × 251¹
LCM(3750,3765) = 941250