What is the Least Common Multiple of 29970 and 29990?

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 29970 and 29990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29970 and 29990, than apply into the LCM equation.

GCF(29970,29990) = 10
LCM(29970,29990) = ( 29970 × 29990) / 10
LCM(29970,29990) = 898800300 / 10
LCM(29970,29990) = 89880030

Least Common Multiple (LCM) of 29970 and 29990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29970 and 29990. First we will calculate the prime factors of 29970 and 29990.

Prime Factorization of 29970

Prime Factorization of 29990

Now multiplying the highest exponent prime factors to calculate the LCM of 29970 and 29990.

LCM(29970,29990) = 2¹ × 3⁴ × 5¹ × 37¹ × 2999¹
LCM(29970,29990) = 89880030