What is the Least Common Multiple of 29760 and 29772?

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 29760 and 29772 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29760 and 29772, than apply into the LCM equation.

GCF(29760,29772) = 12
LCM(29760,29772) = ( 29760 × 29772) / 12
LCM(29760,29772) = 886014720 / 12
LCM(29760,29772) = 73834560

Least Common Multiple (LCM) of 29760 and 29772 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29760 and 29772. First we will calculate the prime factors of 29760 and 29772.

Prime Factorization of 29760

Prime Factorization of 29772

Now multiplying the highest exponent prime factors to calculate the LCM of 29760 and 29772.

LCM(29760,29772) = 2⁶ × 3² × 5¹ × 31¹ × 827¹
LCM(29760,29772) = 73834560