What is the Least Common Multiple of 42380 and 42400?

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 42380 and 42400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42380 and 42400, than apply into the LCM equation.

GCF(42380,42400) = 20
LCM(42380,42400) = ( 42380 × 42400) / 20
LCM(42380,42400) = 1796912000 / 20
LCM(42380,42400) = 89845600

Least Common Multiple (LCM) of 42380 and 42400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42380 and 42400. First we will calculate the prime factors of 42380 and 42400.

Prime Factorization of 42380

Prime Factorization of 42400

Now multiplying the highest exponent prime factors to calculate the LCM of 42380 and 42400.

LCM(42380,42400) = 2⁵ × 5² × 13¹ × 163¹ × 53¹
LCM(42380,42400) = 89845600