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Number Theory Level 2

I have written up all the positive integers less than 1000 that are divisible by 4: 4 , 8 , 12 , 16 , 20 , … , 996. 4, 8, 12, 16, 20, \ldots , 996. I have also written up all the positive integers less than 1000 that are divisible by 6: 6 , 12 , 18 , 24 , 30 , … , 996. 6, 12, 18, 24, 30, \ldots , 996. I notice that 12 and 996 appear in both these sequences.

How many other numbers also appear in both these sequences?


The answer is 81.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Saksham Jain
Nov 19, 2017

WE HAVE TO FIND NOS. WHICH ARE DIVISIBLE BY 12.AS IT IS L c m ( 4 , 6 ) Lcm(4,6) .THEREFORE WE DIVIDE 1000 BY 12 AND TAKE INTEGER PART ANS IS 83 BUT 2 NOS. ARE ALREADY COUNTED THEREFORE ANSWER IS 81

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