Unit 2 · Number Theory

Same HCF and LCM — Another Pair?

Lesson 18 of 18

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About this lesson

Write both numbers as 4m and 4n (since HCF = 4). LCM = 4mn = 40 so mn = 10. The coprime factor pairs of 10 are (1,10) and (2,5). The first gives (4,40) — already given. The second gives (8,20), summing to 28.

Chapters

0:00Introduction

0:22The Question

1:02Unlocking the HCF and LCM Product Rule

1:30Breaking Down the Constraints Systematically

2:12Calculating the Target Sum

2:40Exam Strategy — The Product Clue Exclusion

3:14Confirming the Final Option

Question

The numbers 4 and 40 have highest common factor 4 and lowest common multiple 40. A second pair of numbers also has highest common factor 4 and lowest common multiple 40.

What is the sum of the second pair of numbers?

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Lesson 17

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