Higher January 2022 Paper 1R Q6
6
(a) Work out the lowest common multiple (LCM) of 36 and 120 (2)
\(A = 5^2 \times 7^4 \times 11^p\)
\(B = 5^m \times 7^{n - 5} \times 11\)
\(m\), \(n\) and \(p\) are integers such that
\(m \gt 2\)
\(n \gt 10\)
\(p \gt 1\)
(b) Find the highest common factor (HCF) of \(A\) and \(B\)
Give your answer as a product of powers of its prime factors. (2)
Give your answer as a product of powers of its prime factors. (2)
| Scheme | Marks |
|---|---|
36, 72, 108, ... and 120, 240, 360, ... or 2, 2, 3, 3 and 2, 2, 2, 3, 5 or  | M1 |
| 360 | A1 |
| (2) |
Notes
M1: for any correct valid method e.g.
for starting to list at least three multiples of each number
2, 2, 3, 3 and 2, 2, 2, 3, 5 seen
(may be in a factor tree or a ladder diagram and ignore 1) (Allow 2 × 2 as 4)
or a fully correct “Venn” diagram
A1: or \(2^3 \times 3^2 \times 5\) oe (allow \(2^3 . 3^2 . 5\))
| Scheme | Marks |
|---|---|
| \(5^2 \times 7^4 \times 11\) | B2 |
| (2) | |
| (4 marks) |
Notes
B2: for \(5^2 \times 7^4 \times 11\) (in any order)
(B1 for 660 275 or correct unsimplified product or \(5^a \times 7^b \times 11^c\) where 2 of \(a\), \(b\) and \(c\) are correct)