What is the Least Common Multiple of 460 and 465?

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 460 and 465 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 460 and 465, than apply into the LCM equation.

GCF(460,465) = 5
LCM(460,465) = ( 460 × 465) / 5
LCM(460,465) = 213900 / 5
LCM(460,465) = 42780

Least Common Multiple (LCM) of 460 and 465 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 465. First we will calculate the prime factors of 460 and 465.

Prime Factorization of 460

Prime Factorization of 465

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 465.

LCM(460,465) = 2² × 5¹ × 23¹ × 3¹ × 31¹
LCM(460,465) = 42780