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P4 HCF and LCM: Paper 1 Basics
P4 HCF and LCM: Paper 1 Basics
This paper starts from the definitions: the H.C.F. is the largest common factor and the L.C.M. the smallest common multiple. It then practises direct values, coprime pairs and the shortcut of dividing the product by the H.C.F.
Direct answers Answers: 1 6; 2 10; 3 12; 4 24; 5 5; 6 36; 7 6; 8 1; 9 35; 10 24 is the L.C.M. and the H.C.F. is 4.
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)
- FoundationFind H.C.F.(12, 18).
- FoundationFind H.C.F.(20, 30).
- FoundationFind L.C.M.(4, 6).
- IntermediateFind L.C.M.(6, 8).
- IntermediateFind H.C.F.(15, 25).
- IntermediateFind L.C.M.(9, 12).
- ChallengeWhat is the greatest common factor of 18 and 24?
- ChallengeWhat is H.C.F.(7, 11)?
- ChallengeWhat is L.C.M.(5, 7)?
- Error redoA pupil writes “H.C.F.(8, 12) = 24”. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 6. | The common factors are 1, 2, 3 and 6, so the greatest is 6. |
| 2 | 10. | Both numbers divide by 10 and no larger common factor exists. |
| 3 | 12. | The multiples of 4 and 6 first meet at 12. |
| 4 | 24. | The H.C.F. is 2, and 6 times 8 divided by 2 gives 24. |
| 5 | 5. | Both are multiples of 5 and share no larger factor. |
| 6 | 36. | 9 times 12 divided by the H.C.F. 3 gives 36. |
| 7 | 6. | The largest number dividing both 18 and 24 is 6. |
| 8 | 1, since 1 is their only common factor. | Both are prime, and two coprime numbers always have H.C.F. 1. |
| 9 | 35. | For coprime numbers the L.C.M. is the product: 5 times 7 is 35. |
| 10 | The L.C.M. was written instead: 24 is the L.C.M. of 8 and 12, while the H.C.F. is 4. | The H.C.F. is the greatest common factor and can never exceed either number. |
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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