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A rectangular box measuring 150cm by 156cm by 216cm is to be packed with exact number
of cubes of maximum lengths. Calculate then volume of one such cube
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This problem is to find Greatest Common Divisor (GCD) of the given numbers 150, 156, and 216.
You can decompose the numbers into product of primes
150 = 2*3*5^2,
156 = 2^2*3*13,
216 = 2^3*3^3.
From these decompositions, GCD(150, 156, 216) = 2*3 = 6.
So, the greatest possible cube has the edge of 6 centimeters long and the volume of 6^3 = 216 cm^3.
Solved.