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### Re: Lower Secondary Mathematics

Posted: Sun Jan 24, 2016 3:53 pm
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.

### Re: Lower Secondary Mathematics

Posted: Sun Jan 24, 2016 5:25 pm Hi. Pls help. TIA ### Re: Lower Secondary Mathematics

Posted: Wed Jan 27, 2016 2:58 pm
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

### Re: Lower Secondary Mathematics

Posted: Mon Feb 01, 2016 10:50 am
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?

### Re: Lower Secondary Mathematics

Posted: Mon Feb 01, 2016 3:20 pm
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

### Re: Lower Secondary Mathematics

Posted: Tue Feb 02, 2016 10:52 am
does 2^2 mean 2*2?

### Re: Lower Secondary Mathematics

Posted: Tue Feb 02, 2016 2:05 pm
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 ### Re: Lower Secondary Mathematics

Posted: Tue Feb 02, 2016 10:51 pm
Lisa_Love wrote:does 2^2 mean 2*2?
2^2 means 2 square
2^4 means 2 to the power of 4 ### Re: Lower Secondary Mathematics

Posted: Thu Apr 07, 2016 9:50 pm
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.

### Re: Lower Secondary Mathematics

Posted: Fri Apr 08, 2016 12:26 pm
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.