What is the Least Common Multiple of 84120 and 84138?

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 84120 and 84138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84120 and 84138, than apply into the LCM equation.

GCF(84120,84138) = 6
LCM(84120,84138) = ( 84120 × 84138) / 6
LCM(84120,84138) = 7077688560 / 6
LCM(84120,84138) = 1179614760

Least Common Multiple (LCM) of 84120 and 84138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84120 and 84138. First we will calculate the prime factors of 84120 and 84138.

Prime Factorization of 84120

Prime Factorization of 84138

Now multiplying the highest exponent prime factors to calculate the LCM of 84120 and 84138.

LCM(84120,84138) = 2³ × 3¹ × 5¹ × 701¹ × 37¹ × 379¹
LCM(84120,84138) = 1179614760