## Lower Secondary Mathematics

PSLE marks the graduation of Primary school students and their entry into Secondary schools as teenagers. Discuss all issues about Secondary schooling here.
cftan
OrangeBelt Posts: 64
Joined: Wed Jan 16,

### Re: Lower Secondary Mathematics

jieheng wrote:
insanePaPa wrote:Can someone help my ds on this?

The LCM of 6, 12 & n is 660. Find all possible values of n.
6 = 2 * 3

12=2² * 3

660 = 2² * 3 * 5 * 11

n must include 5 * 11

n = 5 * 11 = 55

n = 2 * 5 * 11 = 110

n = 2² * 5 * 11 = 220

n = 3 * 5 * 11 = 165

n = 2 * 3 * 5 * 11 = 330

n = 2² * 3 * 5 * 11 = 660
Can someone help to explain. Thanks.

YellowBelt Posts: 21
Joined: Tue Jul 10,

### Re: Lower Secondary Mathematics Hi. Pls help. TIA jerrymaths
YellowBelt Posts: 13
Joined: Tue Apr 30,

### Re: Lower Secondary Mathematics

cftan wrote:
jieheng wrote:
insanePaPa wrote:Can someone help my ds on this?

The LCM of 6, 12 & n is 660. Find all possible values of n.
6 = 2 * 3

12=2² * 3

660 = 2² * 3 * 5 * 11

n must include 5 * 11

n = 5 * 11 = 55

n = 2 * 5 * 11 = 110

n = 2² * 5 * 11 = 220

n = 3 * 5 * 11 = 165

n = 2 * 3 * 5 * 11 = 330

n = 2² * 3 * 5 * 11 = 660
Can someone help to explain. Thanks.

NOTE that the way to pick LCM Of several numbers is to take the Highest Number of each prime factor among the three, and then multiply them.

LCM, which is 660, contains two number of 2s, so all three numbers must contain <= two number of 2s, with at least one number having two number of 2s. Since 12 already got two number of 2s,
so n can have zero or one or two number of 2s

Same for 3, LCM contains one 3, so n can have zero or one 3.

LCM contains one 5, but the other two numbers does not have 5, so 5 must come from n. n must contain exactly one 5.
LCM contains one 11, the other two numbers does not have 11, so n must contain one 11.

Combining all these, n must be 5*11 or 5*11*2, 5*11*2*2, 5*11*3, 5*11*2*3, 5*11*2*2*3

This type of questions are quite common in RI and other IP school worksheets. Some are even tougher than this, where they can combine LCM and HCF

Like
"A,B,C are three different integers. A=18,B=60. The lowest common multiple of A,B,C is 540. The highest common factor of A,B,C is 3. Find the possible values of C."

Students need to have a good understanding of how to pick LCM and HCF from prime factorization.

Jerry Guo
Math Program Director -- MaxiMath
We specialize in teaching IP school Math, including Euler Program (RI)
http://www.maximath.sg

BigDevil
ClassMonitor Posts: 9246
Joined: Thu Jul 02,
Total Likes:31

### Re: Lower Secondary Mathematics

The HCF of 2 numbers is 4, and their LCM is 240.
What are the numbers?

Is the answer simply 4 and 240? How do I show it in working?

jerrymaths
YellowBelt Posts: 13
Joined: Tue Apr 30,

### Re: Lower Secondary Mathematics

BigDevil wrote:The HCF of 2 numbers is 4, and their LCM is 240.
What are the numbers?

Is the answer simply 4 and 240? How do I show it in working?
No, there are more possibilities

HCF=4=(2^2)
LCM = 240=(2^4)*3*5

Let the two integers be A,B
So it means one integer should have two number of 2s, the other integer should have 4 number of 2s. Then one integer should have one number of 3, the other should have zero number of 3. One integer should have one number of 5, the other should have zero number of 5.

Combing all these
A = 2^2 , B = 2^4*3*5
OR
A = 2^2 *3, B = 2^4*5
OR
A = 2^2 * 5, B = 2^4*3
OR
A = 2^2 * 3*5, B = 2^4

You can swap values for A,B, but then they are essentially still the same numbers.

Hope it helps.

Jerry Guo
Math Program Director -- MaxiMath
We specialize in teaching IP school Math, including Euler Program (RI)
http://www.maximath.sg

Lisa_Love
KiasuNewbie Posts: 5
Joined: Tue Feb 04,

### Re: Lower Secondary Mathematics

does 2^2 mean 2*2?

BigDevil
ClassMonitor Posts: 9246
Joined: Thu Jul 02,
Total Likes:31

### Re: Lower Secondary Mathematics

jerrymaths wrote:
BigDevil wrote:The HCF of 2 numbers is 4, and their LCM is 240.
What are the numbers?

Is the answer simply 4 and 240? How do I show it in working?
No, there are more possibilities

HCF=4=(2^2)
LCM = 240=(2^4)*3*5 jerrymaths
YellowBelt Posts: 13
Joined: Tue Apr 30,

### Re: Lower Secondary Mathematics

Lisa_Love wrote:does 2^2 mean 2*2?
2^2 means 2 square
2^4 means 2 to the power of 4 cftan
OrangeBelt Posts: 64
Joined: Wed Jan 16,

### Re: Lower Secondary Mathematics

A man travels from town A to town B at an average speed of 4km/h and from town B to town A at an average speed of 6km/h. If he takes 45minutes to complete the entire journey, find his total distance travelled.

iwork
BrownBelt Posts: 621
Joined: Fri Nov 07,
Total Likes:4

### Re: Lower Secondary Mathematics

cftan wrote:A man travels from town A to town B at an average speed of 4km/h and from town B to town A at an average speed of 6km/h. If he takes 45minutes to complete the entire journey, find his total distance travelled.
Distance = Speed x Time.
Time from A to B = Distance/4
Time from B to A = Distance/6

Total time = Distance/4 + Distance/6 = Distance (1/4 + 1/6) = 3/4 hr.

You can then work out the total Distance = Distance x 2.