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Math Help

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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 $x + y + z$

Jan 2, 2019
edited by sudsw12  Jan 3, 2019

#1
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MELODY
CPHILL
ANYONE

POR FAVOR!

Jan 4, 2019
#2
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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

Jan 4, 2019
#3
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Thanks Guest,

Does anyone have the answer for question 1 though?

Jan 5, 2019
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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?

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.

Jan 5, 2019
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Oh I forgot to add the dimensions

4.5 ft by 7.5 ft by 11.25 feet

sudsw12  Jan 5, 2019
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Oh I forgot to add the dimensions

4.5 ft by 7.5 ft by 11.25 feet

I have not thought about it very hard but the HCF of 450, 750 and 1125 is 75

so maybe the answer is 6*9*10=540

Jan 5, 2019