1963 AMC 12 Problem 8

Attempt Problem 8 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The smallest positive integer

x

for which

1260x=N^3,

where

N

is an integer, is:

1050

1260

1260^2

7350

44{,}100

Factor

1260

into primes

Raise every prime exponent to the next multiple of

3

Since

1260=2^2\cdot3^2\cdot5\cdot7,

the least multiplier making every exponent divisible by

3

2\cdot3\cdot5^2\cdot7^2=7350.

Thus, the correct answer is D.

Problem 8 in other years