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Bunuel
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If x, y, and z are positive integers and 2^x*3^y*7^z is divisible by 22 Jun 2022, 09:45
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E
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35% (medium)

Question Stats:

72% (02:02) correct 28% (02:04) wrong based on 327 sessions

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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
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E
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If x, y, and z are positive integers and 2^x*3^y*7^z is divisible by 22 Jun 2022, 12:27
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Could we please get an explanation? Thank you!
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If x, y, and z are positive integers and 2^x*3^y*7^z is divisible by 22 Jun 2022, 16:24
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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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If x, y, and z are positive integers and 2^x*3^y*7^z is divisible by 19 Feb 2025, 05:08
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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
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