find the value of smallest integer n,if 15×n×12 is the product of integers
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Let the numbers be (x-1), x and (x+1).
Their product = x(x^2–1) = 5x12xn = 60n.
If n = 1 the smallest integer then
x(x^2–1) = 60, or
x = 4, as 4(4^2–1) = 4(16–1) = 4*15=60.
So, n = 1 and the three consecutive numbers are 3, 4 and 5.
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