What is the Least Common Multiple of 29748 and 29760?

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 29748 and 29760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29748 and 29760, than apply into the LCM equation.

GCF(29748,29760) = 12
LCM(29748,29760) = ( 29748 × 29760) / 12
LCM(29748,29760) = 885300480 / 12
LCM(29748,29760) = 73775040

Least Common Multiple (LCM) of 29748 and 29760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29748 and 29760. First we will calculate the prime factors of 29748 and 29760.

Prime Factorization of 29748

Prime Factorization of 29760

Now multiplying the highest exponent prime factors to calculate the LCM of 29748 and 29760.

LCM(29748,29760) = 2⁶ × 3¹ × 37¹ × 67¹ × 5¹ × 31¹
LCM(29748,29760) = 73775040