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A sweet shop can pack its whole stock either into boxes of 15 or into boxes of 25, with nothing left over either way. What is the smallest stock the shop can have?

Class 6Playing with NumbersPlaying with Numbers
  • A5
  • B40
  • C75
  • D375

Step-by-Step Solution

The stock has to be a common multiple of 15 and 25, and we want the smallest — the LCM. Since and , the LCM is , which packs as 5 boxes of 15 or 3 boxes of 25. The traps: 5 is the HCF, 40 is 15 + 25, and — the product is the LCM only for co-prime numbers, and these share a 5.
Answer: C) 75

Key idea: Factors come in pairs

To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.

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