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P4 HCF and LCM: Paper 3 Challenge
P4 HCF and LCM: Paper 3 Challenge
This paper is all application: sharing into groups, cutting squares, packing bags, gears lining up and lights flashing together. Decide first whether the situation splits or joins, then choose H.C.F. or L.C.M. before calculating.
Direct answers Answers: 1 15 sets; 2 24 cm; 3 24 days; 4 12 people; 5 3 rounds; 6 60 seconds; 7 4; 8 7 pieces; 9 24 sweets; 10 splitting uses the H.C.F. and coinciding uses the L.C.M.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P4 HCF and LCM |
| Level | P4 |
02 Questions (10 items)
- FoundationShare 60 pens and 45 notebooks into the greatest number of identical sets with nothing left over. How many sets?
- FoundationA 72 cm by 48 cm card is cut into the largest identical squares with no waste. What is the side?
- FoundationA works a duty every 6 days and B every 8 days; both are on duty today. After how many days are they together again?
- IntermediateTeams of 24 and 36 are split into groups of equal and maximal size. How many in each group?
- IntermediateGears of 12 and 18 teeth turn until they line up again. How many rounds does the 12-tooth gear make?
- IntermediateThree lights flash every 3, 4 and 5 seconds. After how many seconds do they flash together again?
- ChallengeHow many common factors do 30 and 45 have?
- ChallengeRopes of 96 cm and 72 cm are cut into equal pieces with the fewest pieces. How many pieces?
- ChallengeA box of sweets can be packed exactly in bags of 8 or in bags of 12. What is the smallest possible number?
- Error redoA pupil says “finding the greatest number of equal shares needs the L.C.M.”. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 15 sets, each with 4 pens and 3 notebooks. | The greatest number of identical sets is the H.C.F. of 60 and 45, which is 15. |
| 2 | 24 cm. | The side is the H.C.F. of the length and breadth: H.C.F.(72, 48) is 24. |
| 3 | 24 days. | Meeting again calls for the L.C.M., and L.C.M.(6, 8) is 24. |
| 4 | 12 people. | The group size divides both 24 and 36, so take the H.C.F. of 12. |
| 5 | 3 rounds. | They align after the L.C.M. of 36 teeth, and 36 divided by 12 is 3. |
| 6 | 60 seconds. | Flashing together needs the L.C.M., and L.C.M.(3, 4, 5) is 60. |
| 7 | 4. | Common factors are the factors of the H.C.F.; 15 has 1, 3, 5 and 15, that is 4. |
| 8 | 7 pieces. | The longest piece is the H.C.F. 24 cm, giving 4 plus 3 pieces. |
| 9 | 24 sweets. | The number must be a multiple of both 8 and 12, so the smallest is the L.C.M. of 24. |
| 10 | The direction is reversed: the greatest number of equal shares, the largest square side and the biggest group all use the H.C.F.; the L.C.M. gives the smallest total or the next time events coincide. | Remember: splitting things apart uses the H.C.F., waiting for events to meet again uses the L.C.M. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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