Foundation June 2024 Paper 3 Q23
23
(a) Two numbers, \(A\) and \(B\), are written as the product of their prime factors.
\(A = 2 \times 3 \times 7^2\)
\(B = 2^3 \times 7\)
Find the lowest common multiple (LCM) of \(A\) and \(B\).
Give your answer as an ordinary number. [2]
(b) A number, \(R\), is written as the product of its prime factors.
\(R = 2 \times 3^2 \times 5 \times k\), where \(k\) is a prime number.
The highest common factor (HCF) of \(R\) and another number, \(P\), is 26.
Find the value of \(k\). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 1176 | 2 | M1 for \(2^3 \times 3 \times 7^2\) oe or for  294, 588, 882, ... AND 56, 112, 168, ... | e.g. \(2 \times 2 \times 2 \times 3 \times 7 \times 7\) Accept no box but need to see A and B |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 13 nfww | 2 | M1 for [26 =] 2 [\(\times\)] 13 oe | For M1 accept 2, 13 or similar possibly seen in a factor tree, diagram etc |