What is the Least Common Multiple of 21720 and 21740?

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 21720 and 21740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21720 and 21740, than apply into the LCM equation.

GCF(21720,21740) = 20
LCM(21720,21740) = ( 21720 × 21740) / 20
LCM(21720,21740) = 472192800 / 20
LCM(21720,21740) = 23609640

Least Common Multiple (LCM) of 21720 and 21740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21720 and 21740. First we will calculate the prime factors of 21720 and 21740.

Prime Factorization of 21720

Prime Factorization of 21740

Now multiplying the highest exponent prime factors to calculate the LCM of 21720 and 21740.

LCM(21720,21740) = 2³ × 3¹ × 5¹ × 181¹ × 1087¹
LCM(21720,21740) = 23609640