What is the Least Common Multiple of 67100 and 67114?

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 67100 and 67114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67100 and 67114, than apply into the LCM equation.

GCF(67100,67114) = 2
LCM(67100,67114) = ( 67100 × 67114) / 2
LCM(67100,67114) = 4503349400 / 2
LCM(67100,67114) = 2251674700

Least Common Multiple (LCM) of 67100 and 67114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67100 and 67114. First we will calculate the prime factors of 67100 and 67114.

Prime Factorization of 67100

Prime Factorization of 67114

Now multiplying the highest exponent prime factors to calculate the LCM of 67100 and 67114.

LCM(67100,67114) = 2² × 5² × 11¹ × 61¹ × 23¹ × 1459¹
LCM(67100,67114) = 2251674700