If x, y, and z are positive integers and 2^x*3^y*7^z is divisible by

Question

If x, y, and z are positive integers and  2^x*3^y*7^z  is divisible by 168 and 441. What is the least value of  x*y*z ?

A. 3
B. 4
C. 5
D. 6
E. 12

AUG1523 · Answer

Could we please get an explanation? Thank you!

MBAHOUSE · Answer

LCM is the least common multiple. If a number is divisible by two numbers is because he is divisible by the LCM of these two numbers. I found the LCM by factoring in prime numbers the two given numbers.

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honorincollable · Answer

To find the answer calculate the GCD:

168 = 2^3*3*7
441 = 3^2*7^2

So GCD(168;441) = 3^2*7^2*2^3
Thus by comparing x=3 y=2 z=2
Hence xyz = 12  answer E

If x, y, and z are positive integers and 2^x3^y7^z is divisible by

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