What is the Least Common Multiple of 21105 and 21112?

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 21105 and 21112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21105 and 21112, than apply into the LCM equation.

GCF(21105,21112) = 7
LCM(21105,21112) = ( 21105 × 21112) / 7
LCM(21105,21112) = 445568760 / 7
LCM(21105,21112) = 63652680

Least Common Multiple (LCM) of 21105 and 21112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21105 and 21112. First we will calculate the prime factors of 21105 and 21112.

Prime Factorization of 21105

Prime Factorization of 21112

Now multiplying the highest exponent prime factors to calculate the LCM of 21105 and 21112.

LCM(21105,21112) = 3² × 5¹ × 7¹ × 67¹ × 2³ × 13¹ × 29¹
LCM(21105,21112) = 63652680