What is the Least Common Multiple of 38800 and 38814?

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 38800 and 38814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38800 and 38814, than apply into the LCM equation.

GCF(38800,38814) = 2
LCM(38800,38814) = ( 38800 × 38814) / 2
LCM(38800,38814) = 1505983200 / 2
LCM(38800,38814) = 752991600

Least Common Multiple (LCM) of 38800 and 38814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38800 and 38814. First we will calculate the prime factors of 38800 and 38814.

Prime Factorization of 38800

Prime Factorization of 38814

Now multiplying the highest exponent prime factors to calculate the LCM of 38800 and 38814.

LCM(38800,38814) = 2⁴ × 5² × 97¹ × 3¹ × 6469¹
LCM(38800,38814) = 752991600