The smallest possible
Number Theory
Level
3
What is the smallest positive integer with the property that it has divisors ending in each of the digits from 0 to 9?
The answer is 270.
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1 solution
who i solved it is that i took the LCM first
so i got
2 2 2 3 3*5
now 5 is must for digits 0 and 5
thinking on 7 as last digit one better route is replace 7 by 3 as 27 (3 3 3) also has 7 as last digit
so reg becomes
2 2 2 3 3 3 5
now for 8 better route is
3 3 2=18
deleting one 2
so i got
2 2 3 3 3 5
now looking at 4 for one good route possible is 3 3 3 2=54
so i got 2 3 3 3 5=270
no more cuttings are possible so it becomes 270