This problem can be solved by using the concept of harmonic progression and the properties of natural numbers.

Step 1:
The problem states that the sum of the reciprocals of three distinct natural numbers is 31/30. This can be written as:

1/a + 1/b + 1/c = 31/30

Step 2:
To simplify the equation, we can multiply each term by abc, which gives us:

bc + ac + ab = 31abc/30

Step 3:
Rearrange the equation to isolate abc:

abc = 30ab + 30ac + 30bc

Step 4:
We are looking for the least possible product of three such natural numbers, so we want to minimize abc. This will occur when a, b, and c are as small as possible.

Step 5:
By trial and error, we can find that the smallest possible values for a, b, and c that satisfy the equation are a=1, b=5, and c=6.

Step 6:
Therefore, the least possible product of three such natural numbers is 1*5*6 = 30.

Question

This problem can be solved by using the concept of harmonic progression and the properties of natural numbers.

Step 1: 
The problem states that the sum of the reciprocals of three distinct natural numbers is 31/30. This can be written as:

1/a + 1/b + 1/c = 31/30

Step 2: 
To simplify the equation, we can multiply each term by abc, which gives us:

bc + ac + ab = 31abc/30

Step 3: 
Rearrange the equation to isolate abc:

abc = 30ab + 30ac + 30bc

Step 4: 
We are looking for the least possible product of three such natural numbers, so we want to minimize abc. This will occur when a, b, and c are as small as possible.

Step 5: 
By trial and error, we can find that the smallest possible values for a, b, and c that satisfy the equation are a=1, b=5, and c=6.

Step 6: 
Therefore, the least possible product of three such natural numbers is 1*5*6 = 30.

Knowee AI · Accepted Answer

This problem can be solved by using the concept of harmonic progression and the properties of natural numbers.

Step 1: 
The problem states that the sum of the reciprocals of three distinct natural numbers is 31/30. This can be written as:

1/a + 1/b + 1/c = 31/30

Step 2: 
To simplify the equation, we can multiply each term by abc, which gives us:

bc + ac + ab = 31abc/30

Step 3: 
Rearrange the equation to isolate abc:

abc = 30ab + 30ac + 30bc

Step 4: 
We are looking for the least possible product of three such natural numbers, so we want to minimize abc. This will occur when a, b, and c are as small as possible.

Step 5: 
By trial and error, we can find that the smallest possible values for a, b, and c that satisfy the equation are a=1, b=5, and c=6.

Step 6: 
Therefore, the least possible product of three such natural numbers is 1*5*6 = 30.

The sum of the reciprocals of three distinct natural numbers is 31/30 . What is the least possible product of three such natural numbers?

Question

The sum of the reciprocals of three distinct natural numbers is $\frac{31}{30}$ . What is the least possible product of three such natural numbers?

Solution

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