What is the Least Common Multiple of 72090 and 72100?

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 72090 and 72100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72090 and 72100, than apply into the LCM equation.

GCF(72090,72100) = 10
LCM(72090,72100) = ( 72090 × 72100) / 10
LCM(72090,72100) = 5197689000 / 10
LCM(72090,72100) = 519768900

Least Common Multiple (LCM) of 72090 and 72100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72090 and 72100. First we will calculate the prime factors of 72090 and 72100.

Prime Factorization of 72090

Prime Factorization of 72100

Now multiplying the highest exponent prime factors to calculate the LCM of 72090 and 72100.

LCM(72090,72100) = 2² × 3⁴ × 5² × 89¹ × 7¹ × 103¹
LCM(72090,72100) = 519768900