What is the Least Common Multiple of 45990 and 46008?

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 45990 and 46008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45990 and 46008, than apply into the LCM equation.

GCF(45990,46008) = 18
LCM(45990,46008) = ( 45990 × 46008) / 18
LCM(45990,46008) = 2115907920 / 18
LCM(45990,46008) = 117550440

Least Common Multiple (LCM) of 45990 and 46008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45990 and 46008. First we will calculate the prime factors of 45990 and 46008.

Prime Factorization of 45990

Prime Factorization of 46008

Now multiplying the highest exponent prime factors to calculate the LCM of 45990 and 46008.

LCM(45990,46008) = 2³ × 3⁴ × 5¹ × 7¹ × 73¹ × 71¹
LCM(45990,46008) = 117550440