What is the Least Common Multiple of 20460 and 20475?

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 20460 and 20475 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20460 and 20475, than apply into the LCM equation.

GCF(20460,20475) = 15
LCM(20460,20475) = ( 20460 × 20475) / 15
LCM(20460,20475) = 418918500 / 15
LCM(20460,20475) = 27927900

Least Common Multiple (LCM) of 20460 and 20475 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20460 and 20475. First we will calculate the prime factors of 20460 and 20475.

Prime Factorization of 20460

Prime Factorization of 20475

Now multiplying the highest exponent prime factors to calculate the LCM of 20460 and 20475.

LCM(20460,20475) = 2² × 3² × 5² × 11¹ × 31¹ × 7¹ × 13¹
LCM(20460,20475) = 27927900