4MA0 Higher January 2012 Paper 4 Q11
11
(a) Find the Highest Common Factor (HCF) of 75 and 90 (2)
(b) Find the Lowest Common Multiple (LCM) of 75 and 90 (2)
| Scheme | Marks |
|---|---|
| \(75 = 3 \times 5^2\) and \(90 = 2 \times 3^2 \times 5\) or 1,3,5,15,25,75 and 1,2,3,5,6,9,10,15,18,30,45,90 or 3 × 5 | M1 |
| 15 | A1 |
| (2) |
Notes
M1: Need not be products of powers; accept products or lists ie 3,5,5 and 2,3,3,5
Prime factors may be shown as factor trees or repeated division
Apart from Questions 3, 13(b) and 17(f) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| \(2 \times 3^2 \times 5^2\) oe eg \(6 \times 3 \times 5^2\) or 75,150,225,300,375,450 and 90,180,270,360,450 | M1 |
| 450 | A1 |
| (2) | |
| (Total 4 marks) |
Notes
M1: Also award for \(\dfrac{75 \times 90}{15}\)