What is the Least Common Multiple of 29952 and 29970?

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 29952 and 29970 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29952 and 29970, than apply into the LCM equation.

GCF(29952,29970) = 18
LCM(29952,29970) = ( 29952 × 29970) / 18
LCM(29952,29970) = 897661440 / 18
LCM(29952,29970) = 49870080

Least Common Multiple (LCM) of 29952 and 29970 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29952 and 29970. First we will calculate the prime factors of 29952 and 29970.

Prime Factorization of 29952

Prime Factorization of 29970

Now multiplying the highest exponent prime factors to calculate the LCM of 29952 and 29970.

LCM(29952,29970) = 2⁸ × 3⁴ × 13¹ × 5¹ × 37¹
LCM(29952,29970) = 49870080