What is the Least Common Multiple of 34944 and 34962?

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 34944 and 34962 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34944 and 34962, than apply into the LCM equation.

GCF(34944,34962) = 6
LCM(34944,34962) = ( 34944 × 34962) / 6
LCM(34944,34962) = 1221712128 / 6
LCM(34944,34962) = 203618688

Least Common Multiple (LCM) of 34944 and 34962 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34944 and 34962. First we will calculate the prime factors of 34944 and 34962.

Prime Factorization of 34944

Prime Factorization of 34962

Now multiplying the highest exponent prime factors to calculate the LCM of 34944 and 34962.

LCM(34944,34962) = 2⁷ × 3¹ × 7¹ × 13¹ × 5827¹
LCM(34944,34962) = 203618688