What is the Least Common Multiple of 74256 and 74272?

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 74256 and 74272 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74256 and 74272, than apply into the LCM equation.

GCF(74256,74272) = 16
LCM(74256,74272) = ( 74256 × 74272) / 16
LCM(74256,74272) = 5515141632 / 16
LCM(74256,74272) = 344696352

Least Common Multiple (LCM) of 74256 and 74272 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74256 and 74272. First we will calculate the prime factors of 74256 and 74272.

Prime Factorization of 74256

Prime Factorization of 74272

Now multiplying the highest exponent prime factors to calculate the LCM of 74256 and 74272.

LCM(74256,74272) = 2⁵ × 3¹ × 7¹ × 13¹ × 17¹ × 11¹ × 211¹
LCM(74256,74272) = 344696352