Foundation January 2022 Paper 1R Q20

EdexcelCurrent spec4 marksProperties of Numbers

(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)

Venn diagram of prime factors: 3 in the 36 circle only; 2, 2, 3 in the overlap; 2 and 5 in the 120 circle only; and a ladder dividing 36 and 120 by 2, 2 and 3 to leave 3 and 10 — Mark scheme (a)

Scheme	Marks
36, 72, 108, ... and 120, 240, 360, ... or 2, 2, 3, 3 and 2, 2, 2, 3, 5 or or \(\dfrac{36 \times 120}{12}\) or 2, 2, 2, 3, 3, 5 oe	M1
360	A1
	(2)

Mark scheme (b)

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)