What is the Least Common Multiple of 21840 and 21854?

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 21840 and 21854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21840 and 21854, than apply into the LCM equation.

GCF(21840,21854) = 14
LCM(21840,21854) = ( 21840 × 21854) / 14
LCM(21840,21854) = 477291360 / 14
LCM(21840,21854) = 34092240

Least Common Multiple (LCM) of 21840 and 21854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21840 and 21854. First we will calculate the prime factors of 21840 and 21854.

Prime Factorization of 21840

Prime Factorization of 21854

Now multiplying the highest exponent prime factors to calculate the LCM of 21840 and 21854.

LCM(21840,21854) = 2⁴ × 3¹ × 5¹ × 7² × 13¹ × 223¹
LCM(21840,21854) = 34092240