What is the Least Common Multiple of 29940 and 29952?

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 29940 and 29952 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29940 and 29952, than apply into the LCM equation.

GCF(29940,29952) = 12
LCM(29940,29952) = ( 29940 × 29952) / 12
LCM(29940,29952) = 896762880 / 12
LCM(29940,29952) = 74730240

Least Common Multiple (LCM) of 29940 and 29952 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29940 and 29952. First we will calculate the prime factors of 29940 and 29952.

Prime Factorization of 29940

Prime Factorization of 29952

Now multiplying the highest exponent prime factors to calculate the LCM of 29940 and 29952.

LCM(29940,29952) = 2⁸ × 3² × 5¹ × 499¹ × 13¹
LCM(29940,29952) = 74730240