What is the Least Common Multiple of 45120 and 45138?

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 45138 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 45138, than apply into the LCM equation.

GCF(45120,45138) = 6
LCM(45120,45138) = ( 45120 × 45138) / 6
LCM(45120,45138) = 2036626560 / 6
LCM(45120,45138) = 339437760

Least Common Multiple (LCM) of 45120 and 45138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45120 and 45138. First we will calculate the prime factors of 45120 and 45138.

Prime Factorization of 45120

Prime Factorization of 45138

Now multiplying the highest exponent prime factors to calculate the LCM of 45120 and 45138.

LCM(45120,45138) = 2⁶ × 3¹ × 5¹ × 47¹ × 7523¹
LCM(45120,45138) = 339437760