# very difficult HCF problem and lcm problems

The following are the exercise questions in a school which I find difficult to solve with my friends please any body help me solve for the children.
Q1) Find two numbers between 100 and 150 that have an HCF of 24.?
Q2) find the least number between 200 and 500 which leaves a remainder of 3 in each case when divided by 8, 10, 12 and 30?
Q3) find the smallest number which when divided by 12, 15, 18 and 27 leaves as remainder 8,11,14 and 23 respectively?
Q4) find the smallest number of 4 digits which when divided by 40, 50 and 60 leaves a remainder of 5 in each case?
Q5) Find the greatest number of 5 digits which when divided by 25, 30 and 40 leaves a remainder of 20, 25 and 35 respectively?
Q6) what is the least number that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18?
Q7) Four bells toll after interval of 8, 9, 12 and 15 minutes, respectively. If they toll together at 3 pm, when will they toll together next?
Original post by frtyu
The following are the exercise questions in a school which I find difficult to solve with my friends please any body help me solve for the children.
Q1) Find two numbers between 100 and 150 that have an HCF of 24.?

Q1) list all the MULTIPLES of 24. when there are two that are between 100 and 150, you've got your answers.

I'm still trying to figure out the others myself for now, i will get back to you if/when i succeed
Also, did you mean it to be "undergraduate" as that may depend on the techniques that can be used?
(edited 12 years ago)
Hints:

Q2: If a number x leaves remainder three on division by all those divisors, what can we say about the remainders if we divide x-3 by those numbers?

Q3: Note that the remainders are four less than the divisors. If x leaves remainder d-4 after being divided by d, then x+4 leaves remainder 0.

Q4: Same as Q2

Q5: Same as Q3

Q6: Just work out the LCM of those numbers and it follows from there.

Q7: Just work out the LCM again...
Q2) find the least number between 200 and 500 which leaves a remainder of 3 in each case when divided by 8, 10, 12 and 30?
Q3) find the smallest number which when divided by 12, 15, 18 and 27 leaves as remainder 8,11,14 and 23 respectively?
Q3)536

mod: merged this thread which is just a repeat of one of the questions in the first post. Ordering has got a little messed up, sorry.
(edited 12 years ago)

How far have you got ?

thank you.but there are some hard probs.i will post later them

please provide step by step baby step solution.

2 eldegee
eldegee thx.but i would want a step by step solution so that i can give to or any student can give those solutions to his/her teacher or in exams.

eldegee you provided procedure but not a solution

these are calss level 7 maths questions.i cant confirm whether its undergraduate or not.
Original post by frtyu
2 eldegee
eldegee thx.but i would want a step by step solution so that i can give to or any student can give those solutions to his/her teacher or in exams.

I think you are mistaking TSR for a homework service.
Original post by frtyu
2 eldegee
eldegee thx.but i would want a step by step solution so that i can give to or any student can give those solutions to his/her teacher or in exams.
Please read the Guide to Posting at the top of the forum.

As others have said, this is not a "do my homework for me" forum. People will help you with problems if you are prepared to put some work in. They are NOT going to provide step-by-step solutions while you do nothing of your own.

Also, do not create new threads in the hope of getting someone else to give you a solution. I will give out warnings if it keeps happening.
I answered these exact questions for you three weeks ago, so how can you still need the answers? (see the second reply in this merged thread).
(edited 12 years ago)
Original post by Forum User
I answered these exact questions for you three weeks ago, so how can you still need the answers? (see the second reply in this merged thread).
Because someone wants something he can just copy and hand in without needing to do any work?

sorry. i wiont repeat.

sorry mod.very sorry.
Q5 -99595
Q6-2160
Q7-9pm
(edited 5 years ago)
shouldnt 3 be 544 because we add the remainder of 4 in the end not subtract to 540
Original post by rijaahsan101
shouldnt 3 be 544 because we add the remainder of 4 in the end not subtract to 540

No, see post #3
Q2)240