What is the Least Common Multiple of 21540 and 21546?

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 21540 and 21546 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21540 and 21546, than apply into the LCM equation.

GCF(21540,21546) = 6
LCM(21540,21546) = ( 21540 × 21546) / 6
LCM(21540,21546) = 464100840 / 6
LCM(21540,21546) = 77350140

Least Common Multiple (LCM) of 21540 and 21546 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21540 and 21546. First we will calculate the prime factors of 21540 and 21546.

Prime Factorization of 21540

Prime Factorization of 21546

Now multiplying the highest exponent prime factors to calculate the LCM of 21540 and 21546.

LCM(21540,21546) = 2² × 3⁴ × 5¹ × 359¹ × 7¹ × 19¹
LCM(21540,21546) = 77350140