What is the Least Common Multiple of 42105 and 42123?

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 42105 and 42123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42105 and 42123, than apply into the LCM equation.

GCF(42105,42123) = 3
LCM(42105,42123) = ( 42105 × 42123) / 3
LCM(42105,42123) = 1773588915 / 3
LCM(42105,42123) = 591196305

Least Common Multiple (LCM) of 42105 and 42123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42105 and 42123. First we will calculate the prime factors of 42105 and 42123.

Prime Factorization of 42105

Prime Factorization of 42123

Now multiplying the highest exponent prime factors to calculate the LCM of 42105 and 42123.

LCM(42105,42123) = 3¹ × 5¹ × 7¹ × 401¹ × 19¹ × 739¹
LCM(42105,42123) = 591196305