What is the Least Common Multiple of 45120 and 45135?

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 45120 and 45135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45120 and 45135, than apply into the LCM equation.

GCF(45120,45135) = 15
LCM(45120,45135) = ( 45120 × 45135) / 15
LCM(45120,45135) = 2036491200 / 15
LCM(45120,45135) = 135766080

Least Common Multiple (LCM) of 45120 and 45135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45120 and 45135. First we will calculate the prime factors of 45120 and 45135.

Prime Factorization of 45120

Prime Factorization of 45135

Now multiplying the highest exponent prime factors to calculate the LCM of 45120 and 45135.

LCM(45120,45135) = 2⁶ × 3² × 5¹ × 47¹ × 17¹ × 59¹
LCM(45120,45135) = 135766080