What is the Least Common Multiple of 34320 and 34335?

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 34320 and 34335 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34320 and 34335, than apply into the LCM equation.

GCF(34320,34335) = 15
LCM(34320,34335) = ( 34320 × 34335) / 15
LCM(34320,34335) = 1178377200 / 15
LCM(34320,34335) = 78558480

Least Common Multiple (LCM) of 34320 and 34335 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34320 and 34335. First we will calculate the prime factors of 34320 and 34335.

Prime Factorization of 34320

Prime Factorization of 34335

Now multiplying the highest exponent prime factors to calculate the LCM of 34320 and 34335.

LCM(34320,34335) = 2⁴ × 3² × 5¹ × 11¹ × 13¹ × 7¹ × 109¹
LCM(34320,34335) = 78558480