The HCF of two numbers is 5 and their LCM is 300. If the sum of the two numbers is 85, what is their difference?

35Correct answerYour answer60Correct answerYour answer85Correct answerYour answer295Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Product = $\operatorname{HCF} \times \operatorname{LCM} = 5 \times 300 = 1{,}500$ .
The numbers are 5a and 5b with $a + b = 17$ and ab = 60 (co-prime).
a and b are 5 and 12, so the numbers are 25 and 60.
Difference = $60 - 25 = 35$ .

Worth noting

60 is the larger number and 85 the sum; 295 is $\operatorname{LCM} - \operatorname{HCF}$ . Check: $\operatorname{HCF}(25, 60) = 5$ and $\operatorname{LCM}(25, 60) = 300$ . Quicker: $(x - y)^2 = (x + y)^2 - 4xy = 7225 - 6000 = 1225$ , so the difference is 35.

Concept: Using sum and product together with HCF and LCM
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsFinding HCF and LCM

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The HCF of two numbers is 5 and their LCM is 300. If the sum of the two numbers is 85, what is their difference?

Explanation