What is the Least Common Multiple of 20475 and 20480?

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 20475 and 20480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20475 and 20480, than apply into the LCM equation.

GCF(20475,20480) = 5
LCM(20475,20480) = ( 20475 × 20480) / 5
LCM(20475,20480) = 419328000 / 5
LCM(20475,20480) = 83865600

Least Common Multiple (LCM) of 20475 and 20480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20475 and 20480. First we will calculate the prime factors of 20475 and 20480.

Prime Factorization of 20475

Prime Factorization of 20480

Now multiplying the highest exponent prime factors to calculate the LCM of 20475 and 20480.

LCM(20475,20480) = 3² × 5² × 7¹ × 13¹ × 2¹²
LCM(20475,20480) = 83865600