There are some stickers in a box. The stickers can be put into packets of 4 or 6 with no stickers left over. When the stickers are put into packets of 9, there are 3 stickers left over. What is the smallest possible number of stickers in the box?
Need a hint?
Start by listing the multiples of 4 and 6 to find the smallest number that both can divide into exactly. Then check if that number leaves a remainder of 3 when divided by 9.
Worked answer
- Find the smallest number that can be divided by 4 and 6 exactly.
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
- Multiples of 6: 6, 12, 18, 24, ...
- The smallest common multiple is 12.
- Check: 12 ÷ 9 = 1 remainder 3.
- So the smallest possible number of stickers is 12.
The mistake this question tests
Factors and multiples (HCF, LCM)
Pupils sometimes pick a larger common multiple such as 24 or 36 without checking the remainder: 24 ÷ 9 leaves 6 and 36 ÷ 9 leaves 0.
How to fix it at home →Wrong answers children often give:
- 24 Factors and multiples (HCF, LCM)
- 36 Factors and multiples (HCF, LCM)
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