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If the product of two positive integers . . .

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If the product of two positive integers . . .

by Vincen » Tue Dec 19, 2017 7:35 am
If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?

I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9

A. I only
B. II and III only
C. I and II only
D. I and III only
E. I, II and III

The OA is option A.

What are the calculations I should make to get an answer here? Experts, do I have to make a list? I don't know how to solve it. Help. <i class="em em-disappointed"></i>
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by [email protected] » Tue Dec 19, 2017 12:39 pm
Hi Vincen,

We're told that If the product of two positive integers is 144. We're asked which of the following COULD be the LCM and HCF of the two numbers.

To start, it would help to list out the possible pairs of integers (while this might seem like a lot of work, there are patterns that you can take advantage of - for example, since 4 and 36 are factors, we can 'double' the 4 and 'halve' the 36 to quickly find that 8 and 18 are also factors):

1 and 144
2 and 72
3 and 48
4 and 36
6 and 24
8 and 18
9 and 16
12 and 12

I. LCM : 24; HCF : 6

The LCM could be 24 and the HCF could be 6 if the two values are 6 and 24.
Roman Numeral 1 COULD be true. Eliminate Answer B.

II. LCM : 18; HCF : 8

No pair of numbers in this list has an LCM of 18 (the LCM of 8 and 18 is 72).
Roman Numeral 2 is NOT true. Eliminate Answers C and E.

III. LCM : 16; HCF : 9

No pair of numbers in this list has an LCM of 16 (the LCM of 9 and 16 is 144).
Roman Numeral 3 is NOT true. Eliminate Answer D.

Final Answer: A

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