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# Number Theory

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Fill in the blanks with three distinct positive integers.

1/___ + 1/___ + 1/___ = \frac{13}{12}

Jun 20, 2024

#1
+1230
+1

We want the blanks to be 3 numbers that have a least common multiple of 12.

We also want them to be as small as possible, but we don't want them to be 1, since that would make this problem impossible.

The numbers $$2,3,4$$ satsify these conditions. We have

$$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$$

Converting them to the same denominator of 12, we get

$$6/12+4/12+3/12 = 13/2$$

So 2, 3,4 is our answer.

Thanks! :)

Jun 20, 2024

#1
+1230
+1

We want the blanks to be 3 numbers that have a least common multiple of 12.

We also want them to be as small as possible, but we don't want them to be 1, since that would make this problem impossible.

The numbers $$2,3,4$$ satsify these conditions. We have

$$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$$

Converting them to the same denominator of 12, we get

$$6/12+4/12+3/12 = 13/2$$

So 2, 3,4 is our answer.

Thanks! :)

NotThatSmart Jun 20, 2024