Which is the greatest 6-digit number divisible by 4, 8, 10, 6, 9, 15, 45, 24, 36 and 20?
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When a number N is divisible by 4 , 6 , 8 , 9 , 1 0 , 1 5 , 2 0 , 2 4 , 3 6 , and 4 5 means that N is divisible by the lowest common multiple of 4 , 6 , 8 , 9 , 1 0 , 1 5 , 2 0 , 2 4 , 3 6 , and 4 5 . And lcm ( 4 , 6 , 8 , 9 , 1 0 , 1 5 , 2 0 , 2 4 , 3 6 , 4 5 ) = 2 3 × 3 2 × 5 = 3 6 0 .
The greatest 6-digit divisible by 3 6 0 is ⌊ 3 6 0 1 0 0 0 0 0 0 ⌋ × 3 6 0 = 2 7 7 7 × 3 6 0 = 9 9 9 7 2 0 .
Notation: ⌊ ⋅ ⌋ denotes the floor function .