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P4 HCF and LCM: Paper 2 Intermediate
P4 HCF and LCM: Paper 2 Intermediate
This paper drills short division for two and three numbers, then uses the rule that the product equals H.C.F. times L.C.M. to recover an unknown value, and settles the bounds on an H.C.F.
Direct answers Answers: 1 12; 2 15; 3 36; 4 72; 5 24; 6 60; 7 18; 8 14; 9 72; 10 the H.C.F. may equal one of the numbers.
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)
- FoundationUse short division to find H.C.F.(36, 48).
- FoundationFind H.C.F.(45, 60, 75).
- FoundationFind L.C.M.(12, 18).
- IntermediateFind L.C.M.(8, 12, 18).
- IntermediateFind H.C.F.(48, 72).
- IntermediateFind L.C.M.(10, 15, 20).
- ChallengeTwo numbers have H.C.F. 6 and L.C.M. 36; one of them is 12. What is the other?
- ChallengeFind H.C.F.(42, 56).
- ChallengeFind L.C.M.(24, 36).
- Error redoA pupil says “the H.C.F. is always less than both numbers”. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 12. | Dividing both by 12 leaves 3 and 4, which share no factor other than 1, so the H.C.F. is 12. |
| 2 | 15. | All three divide by 15, and 3, 4 and 5 share no common factor. |
| 3 | 36. | 12 times 18 divided by the H.C.F. 6 gives 36. |
| 4 | 72. | The L.C.M. of 8 and 12 is 24, and pairing that with 18 gives 72. |
| 5 | 24. | Short division is left with 2 and 3, and the factors taken out multiply to 24. |
| 6 | 60. | The L.C.M. of 10 and 15 is 30, and 30 with 20 gives 60. |
| 7 | 18. | The product equals H.C.F. times L.C.M.: 216 divided by 12 is 18. |
| 8 | 14. | Dividing both by 14 leaves 3 and 4, so the H.C.F. is 14. |
| 9 | 72. | The H.C.F. is 12, and 24 times 36 divided by 12 is 72. |
| 10 | Not always: H.C.F.(9, 9) is 9, equal to the number itself; the H.C.F. never exceeds the smaller number. | The H.C.F. is strictly smaller than both numbers only when the two numbers differ. |
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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