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###### very difficult HCF problem and lcm problems

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12 years ago

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.?

ANSWERS: Q) 120 and 144

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?

ANSWERS: Q2)243 Q3)536 Q4)1205

Q1) Find two numbers between 100 and 150 that have an HCF of 24.?

ANSWERS: Q) 120 and 144

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?

ANSWERS: Q2)243 Q3)536 Q4)1205

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.?

ANSWERS: Q) 120 and 144

Q1) Find two numbers between 100 and 150 that have an HCF of 24.?

ANSWERS: Q) 120 and 144

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)

Reply 2

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: 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?

answer: Q2)243

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.

answer: Q2)243

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)

Reply 10

12 years ago

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.

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.

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.

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.

Reply 12

12 years ago

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).

Reply 17

2 years ago

shouldnt 3 be 544 because we add the remainder of 4 in the end not subtract to 540

Reply 18

2 years ago

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

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