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Richard cuts a rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?

Determine the largest possible integer \(n\) such that $942!$ is divisible by $60^n$

$x, y,$ and $z$ are positive integers such that $\gcd(x,y,z)=14$ and $\text{lcm}(x,y,z)=630.$ What is the smallest possible value of $x + y + z$

sudsw12 Jan 2, 2019

#2**+1 **

Determine the largest possible integer such that $942!$ is divisible by $60^n$

**942! mod 60^233 =0**

$x, y,$ and $z$ are positive integers such that $\gcd(x,y,z)=14$ and $\text{lcm}(x,y,z)=630.$ What is the smallest possible value of $x + y + z$

x = 14, y =70, z =126

LCM[14, 70, 126] = 630

GCD[14, 70, 126] = 14

x + y + z =14 + 70 + 126 =210

Guest Jan 4, 2019

#4**+2 **

Richard cuts a rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?

It would depend on the dimensions of the prism.

Technically a cube **is** a rectangular prism so if the rectangular prism in the question is a cube then the answer is 1.

Melody Jan 5, 2019