A number theory problem by Rakibul Hasan Emon
Number Theory
Level
2
are 3 positive integers whose sum is 10 and their lowest common multiple is 30.
What can we conclude about these 3 numbers?
They are all irrational numbers
They are all prime numbers
They are all odd numbers
They are all even numbers
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If the g.c.m. is 30 then one of them must have 5 among his factors: 10 is to high due to the fact that the sum is 10 so it must be 5. The same we can say about the 3 as factor: 6 is too high because 5+6=11 then the second number is 3. 10-3-5=2 then 2 is the third number.