If x , y and z are positive integer and 3 x = 4 y = 7 z ,

Kaiden Wilkins

Kaiden Wilkins

Answered question

2022-05-17

If x, y and z are positive integer and 3 x = 4 y = 7 z, then What is the least possible value of x + y + z?

Answer & Explanation

aliasjuliankso9y

aliasjuliankso9y

Beginner2022-05-18Added 11 answers

Since x, y and z are integers and positive, and 3, 4 and 7 are coprime, x must contain 4 and 7 as factors (that is, the minimum value for x is 28), y must contain 3 and 7 (21) and z must contain 3 and 4 (12) Then 3*(4*7*n)=4*(3*7*m)=7*(4*3*p), where m,n and p are positive integers So the least possible value for x+y+z is when n=m=p=1 and x+y+z=28+21+12
tuehanhyd8ml

tuehanhyd8ml

Beginner2022-05-19Added 5 answers

Hint : Think of 3x , 4y and 7z as surfaces in x y z plane and your are trying to find out the the common point of intersection of these surfaces . If there are more than one you select the least

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