What is the Least Common Multiple of 53100 and 53109?

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 53100 and 53109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53100 and 53109, than apply into the LCM equation.

GCF(53100,53109) = 9
LCM(53100,53109) = ( 53100 × 53109) / 9
LCM(53100,53109) = 2820087900 / 9
LCM(53100,53109) = 313343100

Least Common Multiple (LCM) of 53100 and 53109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53100 and 53109. First we will calculate the prime factors of 53100 and 53109.

Prime Factorization of 53100

Prime Factorization of 53109

Now multiplying the highest exponent prime factors to calculate the LCM of 53100 and 53109.

LCM(53100,53109) = 2² × 3³ × 5² × 59¹ × 7¹ × 281¹
LCM(53100,53109) = 313343100