What is the Least Common Multiple of 30090 and 30109?

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 30090 and 30109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30090 and 30109, than apply into the LCM equation.

GCF(30090,30109) = 1
LCM(30090,30109) = ( 30090 × 30109) / 1
LCM(30090,30109) = 905979810 / 1
LCM(30090,30109) = 905979810

Least Common Multiple (LCM) of 30090 and 30109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30090 and 30109. First we will calculate the prime factors of 30090 and 30109.

Prime Factorization of 30090

Prime Factorization of 30109

Now multiplying the highest exponent prime factors to calculate the LCM of 30090 and 30109.

LCM(30090,30109) = 2¹ × 3¹ × 5¹ × 17¹ × 59¹ × 30109¹
LCM(30090,30109) = 905979810