What is the Least Common Multiple of 21814 and 21834?

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 21814 and 21834 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21814 and 21834, than apply into the LCM equation.

GCF(21814,21834) = 2
LCM(21814,21834) = ( 21814 × 21834) / 2
LCM(21814,21834) = 476286876 / 2
LCM(21814,21834) = 238143438

Least Common Multiple (LCM) of 21814 and 21834 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21814 and 21834. First we will calculate the prime factors of 21814 and 21834.

Prime Factorization of 21814

Prime Factorization of 21834

Now multiplying the highest exponent prime factors to calculate the LCM of 21814 and 21834.

LCM(21814,21834) = 2¹ × 13¹ × 839¹ × 3² × 1213¹
LCM(21814,21834) = 238143438