What is the Least Common Multiple of 45972 and 45990?

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 45972 and 45990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45972 and 45990, than apply into the LCM equation.

GCF(45972,45990) = 18
LCM(45972,45990) = ( 45972 × 45990) / 18
LCM(45972,45990) = 2114252280 / 18
LCM(45972,45990) = 117458460

Least Common Multiple (LCM) of 45972 and 45990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45972 and 45990. First we will calculate the prime factors of 45972 and 45990.

Prime Factorization of 45972

Prime Factorization of 45990

Now multiplying the highest exponent prime factors to calculate the LCM of 45972 and 45990.

LCM(45972,45990) = 2² × 3² × 1277¹ × 5¹ × 7¹ × 73¹
LCM(45972,45990) = 117458460