What is the Least Common Multiple of 29970 and 29988?

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 29988 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 29988, than apply into the LCM equation.

GCF(29970,29988) = 18
LCM(29970,29988) = ( 29970 × 29988) / 18
LCM(29970,29988) = 898740360 / 18
LCM(29970,29988) = 49930020

Least Common Multiple (LCM) of 29970 and 29988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29970 and 29988. First we will calculate the prime factors of 29970 and 29988.

Prime Factorization of 29970

Prime Factorization of 29988

Now multiplying the highest exponent prime factors to calculate the LCM of 29970 and 29988.

LCM(29970,29988) = 2² × 3⁴ × 5¹ × 37¹ × 7² × 17¹
LCM(29970,29988) = 49930020