What is the Least Common Multiple of 35100 and 35109?

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 35100 and 35109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35100 and 35109, than apply into the LCM equation.

GCF(35100,35109) = 9
LCM(35100,35109) = ( 35100 × 35109) / 9
LCM(35100,35109) = 1232325900 / 9
LCM(35100,35109) = 136925100

Least Common Multiple (LCM) of 35100 and 35109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 35100 and 35109. First we will calculate the prime factors of 35100 and 35109.

Prime Factorization of 35100

Prime Factorization of 35109

Now multiplying the highest exponent prime factors to calculate the LCM of 35100 and 35109.

LCM(35100,35109) = 2² × 3³ × 5² × 13¹ × 47¹ × 83¹
LCM(35100,35109) = 136925100