What is the Least Common Multiple of 42705 and 42720?

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 42705 and 42720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42705 and 42720, than apply into the LCM equation.

GCF(42705,42720) = 15
LCM(42705,42720) = ( 42705 × 42720) / 15
LCM(42705,42720) = 1824357600 / 15
LCM(42705,42720) = 121623840

Least Common Multiple (LCM) of 42705 and 42720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42705 and 42720. First we will calculate the prime factors of 42705 and 42720.

Prime Factorization of 42705

Prime Factorization of 42720

Now multiplying the highest exponent prime factors to calculate the LCM of 42705 and 42720.

LCM(42705,42720) = 3² × 5¹ × 13¹ × 73¹ × 2⁵ × 89¹
LCM(42705,42720) = 121623840