Foundation January 2021 Paper 1R Q24
24 \(A = 2^8 \times 3^5 \times 11^4 \qquad B = 2^6 \times 3 \times 11^8\)
(a) Find the highest common factor (HCF) of \(A\) and \(B\). (2)
(b) Find the lowest common multiple (LCM) of \(2A\) and \(3B\).
Give the LCM as a product of powers of its prime factors. (2)
Give the LCM as a product of powers of its prime factors. (2)
| Scheme | Marks |
|---|---|
| \(2^6 \times 3 \times 11^4\) | B2 |
| (2) |
Notes
B2: oe, accept 2 811 072
(B1 for \(2^a \times 3^b \times 11^c\) oe where two of \(a\), \(b\) and \(c\) are correct)
| Scheme | Marks |
|---|---|
| \(2^9 \times 3^5 \times 11^8\) | B2 |
| (2) | |
| (4 marks) |
Notes
B2: cao
(B1 for \(2^a \times 3^b \times 11^c\) oe where two of \(a\), \(b\) and \(c\) are correct or \(2.666... \times 10^{13}\) or an equivalent expression for e.g. \(2^2 \times 2^7 \times 3^5 \times 11^3 \times 11^5\))