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# Numbers – Remember What They Taught You In Primary School?

(13)
Tuition given in the topic of E-Maths Tuition Questions from the desk of at 6:36 pm (Singapore time)

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Maths is all about foundation. Thus Miss Loi is sometimes a little disappointed that many students got themselves stuck in the question below. This question appears almost without fail and is meant to test your basics from primary school to Secondary One.

The numbers 60 and 126, written as products of their prime factors are:

60 = 22 x 3 x 5
126 = 2 x 32 x 7

Find

1. the largest integer which is a factor of both 60 and 126.
2. the smallest integer which is an exact multiple of both 60 and 126.
3. the smallest integer k such that 126k is a perfect square.
4. the smallest integer value of m for which 60m is a multiple of 126.

P.S. If you’re still stuck remember to look for Miss Loi’s primary school teacher friends Miss Hau Chu Fen and Mdm Lau Chio Min.

### Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

1. NTT commented in tuition class

2007
Apr
16
Mon
8:30pm

1

Err...

120 = 2 x 3^2 x 7?

should be 126.. i think.

2. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Apr
16
Mon
8:45pm

2

Arigato gozaimasu NTT-san!

Everywhere it says 126 except the spot you highlighted ... sigh ... need to chase the optician for that new pair of glasses soon!

3. NTT commented in tuition class

2007
Apr
17
Tue
11:15pm

3

Hehe.. NP.. Can I answer?? :p (Feels soooo secondary school... hehe)

1. 2 x 3 = 6
2. 2 x 2 x 3 x 3 x 5 x 7 = 1260
3. 2 x 7 = 17
4. 3 x 7 = 21

4. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Apr
18
Wed
10:25am

4

Tupolev,

Of coz you will feel like sec sch - Miss Loi already mentioned this is a Sec One question!

No sweat right? Sigh ... but still many students got this wrong. But then again you're overaged! Bully kechil izit??!

BTW thanx for dropping by again 🙂

5. yk commented in tuition class

2007
Apr
29
Sun
1:18am

5

2 x 7 = 17 ??

Minus mark for wrong answer, but still get working marks. (=

6. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Apr
29
Sun
8:25pm

6

yk, actually to Miss Loi the LHS is the more important portion which normally means that the RHS is just a formality *excuses herself for not checking properly* but having said that THIS IS AN UNFORGIVEABLE SLAP-YOUR-HAND WHAT-A-PITY WHAT-A-WASTE HOW-ON-EARTH-COULD THIS HAPPEN CARELESS MISTAKE!!!!

7. Prodigy commented in tuition class

2007
Oct
14
Sun
9:32pm

7

Miss Loi, care to explain 3 and 4 to me? thanks.

8. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
15
Mon
12:00am

8

Hey Prodigy,

Thanks for rekindling this post from the early days, when Miss Loi was just a budding blogger making her first baby steps into the blogging world (and she still is) ...

Anyway to explain this better ...

First of all do understand that part 1 deals with HCF and part 2 deals with LCM.

For part 3, you need to find the least value of k such that 126 x k is a perfect square (i.e. can be square-rooted, if there's such a word :P).

For a number to be a perfect square, there must be at least two of each of its factors.

Hence for 126 = 2 x 3 x 3 x 7, we need at least another 2 and 7 to 'complete the square' (i.e. make it into 2 x 2 x 3 x 3 x 7 x 7). So k must be 2 x 7 = 14.

9. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
15
Mon
12:09am

9

Part 4 is a little tricky, so let's explain this one step at a time.

i. 60m is a multiple of 126. But obviously 60m is also a multiple of 60!

ii. By this definition, do you agree that when m is at its 'smallest integer value for which 60m is a multiple of 126', this implies that 60m IS the LCM of both 60 and 126?

iii. The LCM of both 60 and 126 is 2 x 2 x 3 x 3 x 5 x 7 (obtained in part 2). So we can equate:

60m = 2 x 2 x 3 x 3 x 5 x 7
m = (2 x 2 x 3 x 3 x 5 x 7)/(2 x 2 x 3 x 5)

... cancel here ... cancel there ...

m = 3 x 7 = 21

10. Jala commented in tuition class

2007
Dec
20
Thu
1:40am
11. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Dec
20
Thu
1:55pm

11

Hi Jala, LCM = Lowest Common Multiple. Care to elaborate on which part do you not understand?

12. MathsRock commented in tuition class

2009
Oct
11
Sun
4:19pm

12

*For no.1, find HCF, which is 2x3 = 6.
*For no.2, find LCM, which is 2squarex3squarex5x7 = 1260.
*For no.3:
The prime factors of 126 is 2x3squarex7.
2 and 7 is not a perfect square, so make 2 and 7 become, 2square and 7square. So just add another 2 and another 7. So k is = 2x7 = 14.
*For no.4, if you how to do no.2, you should know how to do this.
Simply, 1260 divide by 60 = 21.

Correct? (:

13. michelle commented in tuition class

2009
Nov
9
Mon
10:06pm
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