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A man has a certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a parcel he is left with one box; if he packs 7 in a parcel, none is left over. What is the number of boxes, he may have to pack ?

A man has a certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a parcel he is left with one box; if he packs 7 in a parcel, none is left over. What is the number of boxes, he may have to pack ? Correct Answer 301

Concept Used 

To find the LCM of numbers are given and find that number which is divide by another number 

Calculation 

We know that, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7.

LCM of (3, 4, 5, 6)  = 60 

so, number in the form = 60x + 1

Now, consider the value of x to form a number, so that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7.

⇒ for, x = 5 

Number = 60 × 5 + 1 = 301 

∴ 301 is divisible by 7 

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