Question

Find the smallest integer n so that 5×12×n is the product of 3consecutive integers

Answer 1

$5 \times 12 \times n \\ = 3 \times 4 \times 5 \times n$
Now 3,4 and 5 are consecutive numbers, so possible values for n are 2 and 6. But since the required number is product of 3 consecutive numbers, n can only be equal to 1.
$n = 1$
And the number is
$3\times 4 \times 5=60$