What is the Least Common Multiple of 29904 and 29920?

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 29904 and 29920 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29904 and 29920, than apply into the LCM equation.

GCF(29904,29920) = 16
LCM(29904,29920) = ( 29904 × 29920) / 16
LCM(29904,29920) = 894727680 / 16
LCM(29904,29920) = 55920480

Least Common Multiple (LCM) of 29904 and 29920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29904 and 29920. First we will calculate the prime factors of 29904 and 29920.

Prime Factorization of 29904

Prime Factorization of 29920

Now multiplying the highest exponent prime factors to calculate the LCM of 29904 and 29920.

LCM(29904,29920) = 2⁵ × 3¹ × 7¹ × 89¹ × 5¹ × 11¹ × 17¹
LCM(29904,29920) = 55920480