Ms Sia’s Realm of Maths

More Practice/Help on HCF & LCM Problem Sums

Posted on: May 11, 2009

Problem sums on HCF and LCM can be really tricky as they are not easy to identify. Thus for this post, the main focus is not on going through how to find HCF and LCM (please refer to your notes on those), but more importantly to go through how to determine when to find the HCF and when to find the LCM of the numbers involved in the problem sums.

There will be some problem sums for you to try out at the end of the post, but first let’s take a look at a typical problem involving the HCF.

HCF – A Typical Problem

3 strings of different lengths, 240 cm, 318 cm and 426 cm are to be cut into equal lengths. What is the greatest possible length of each piece?

If you notice, finding the HCF is crucial here because you are trying to find what the 3 numbers have in common, i.e. a common factor. All 3 numbers must be able to be divided by the same number in order for all 3 strings to be cut into equal lengths. HCF is needed here because you are asked to find the greatest possible length.


LCM – A Typical Problem

Two lighthouses flash their lights every 20s and 30s respectively. Given that they flashed together at 7pm, when will they next flash together?

One method to finding the next time the lighthouses flash together is:

20, 40, 60

30, 60, 90

60 is a multiple common to 20 and 30, and thus the lighthouses will flash together in 60s’ time, i.e. at 7:01pm.

This is the same as finding the lowest common multiple, or LCM:

There are other different types of problems involving LCM, but just remember that such questions involve you trying to find a multiple that is common to the numbers involved.

Try out the problem sums below and see if you get them right! The starred ones require a little more thinking šŸ˜‰

1. As a humanitarian effort, food ration is distributed to each refugee in a refugee camp. If a day’s ration is 284 packets of biscuits, 426 packets of instant noodles and 710 bottles of water, how many refugees are there in the camp? [142 refugees]

2. 294 blue balls, 252 pink balls and 210 yellow balls are distributed equally among some students with none left over. What is the biggest possible number of students? [42 students]

3. A group of girls bought 72 rainbow hairbands, 144 brown and black hairbands, and 216 bright-coloured hairbands. What is the largest possible number of girls in the group? [72 girls]

4. A man has a garden measuring 84 m by 56 m. He wants to divide them equally into the minimum number of square plots. What is the length of each square plot? [28 m]

5. Leonard wants to cut identical square as big as he can from a piece of paper 168 mm by 196 mm. What is the length of each square? [28 cm]

6.* 32 girls and 52 boys were on an overseas learning trip, and they were divided into as many groups as possible where the number of groups of girls and the number of groups of boys are the same. How many girls and how many boys are there in each group? [8 girls, 13 boys]

7. A small bus interchange has 2 feeder services that start simultaneously at 9am. Bus number 801 leaves the interchange at 15-min intervals, while bus number 802 leaves at 20-min intervals. On a particular day, how many times did both services leave together from 9 am to 12 noon inclusive? [4 times]

8. Candice, Gerald and Johnny were jumping up a flight of stairs. Candice did 2 steps at a time, Gerald 3 steps at time while Johnny 4 steps at a time. If they started on the bottom step at the same, on which step will all 3 land together the first time? [12th step]

9. Heidi helps out at her mum’s stall every 9 days while her sister every 3 days. When will they be together if they last helped out on June 16 2008? [June 25 2008]

10. A group of students can be further separated into groups of 5, 13 and 17. What is the smallest possible total number of students? [1105 students]

11. Jesslyn goes to the market every 64 days. Christine goes to the same market every 72 days. They met each other one day. How many days later will they meet each other again? [576 days]

12.*Mrs Goh and 3 of her friends went to a supermarket and found that a package of 6 dishcloths cost $10. If they were to share the purchase such that each has the same number of dishcloths, what is the minimum amount each has to pay? [$5]


41 Responses to "More Practice/Help on HCF & LCM Problem Sums"

This was just what i was looking for. Can you help with adding and subtracting integers without the number line?

Hi there. Do look under “More Practice on Arithmetic Sums”.

I want practice on H.C.F and L.C.M as my term examinations are on the 14th of september . Please could you help me ?

the lcm of 2 nos. is 432and hcf is 72 if 1 no. is 144 find the other !! ?? can u pls help me out with this 1

thanks for providing the information.this is very helpful for my preperation

There is a very easy solution for ur quest abhijit
just C here
let 2 no’s be x1 and x2
now u hav x1=144
There4 the other no is 216…

thanx a lot

as my maths teacher is very rude this helped me to wipe off my doubts

hey ms sia, i don’t know who you are..! but whatever u are doing here is just AWSOMMMEEE..! m so much impressed..! i have never got that much explained ‘explanation’ in ma life..! the problems u’ve included here increases the gamut of thinking. i want to be like you SOMEDAY..! šŸ™‚ thanks a lottttttt..!

Hi Luvy, thank you very much šŸ™‚ I’m glad that you’re inspired. Where do you hail from?

hi, well, i hail from india, new delhi vicinity.
and i am hooked to ur blog now (and that’s going to last for a long time)..! i love ur teaching method coz in our education system (as a whole) much emphasis is given to rote learning and to the question “how many marks u’ve got in maths ‘subject’?
they never allow to LOVE the subject.., what m feeling first time !:)
hey plz keep it going and be ma (permanent) maths teacher..!

Can u post how to do a sum like this:
Find the greastest number which divides 34, 60, and 85 leaving remainders of 7, 6, and 4 respectievly

Hi Persias

this is in answer to your question asked on 22 june 2010 i know its really late and you might have received the answer from any other source still i am giving some explanation :
Simply subtract 7,6,4 from 34,60,85 respectively and you will obtain
27,54,81 and find hcf of these nos you will find 27 as the answer.
you may also check your answer by dividing by 27 to the given numbers.

you should describe the question more easy way thanks

Thanks! very good problems..

can you explain me why find hcf of this Q
a farmer to put 39 kg wheat 404 kg ots barleyinto largest bags of = size that wll hold exactly of each kind. hw msny kgs must each bag hold.

traffic light at three different road crossing change after 45 sec,50 sec and 72 what time will they change together again if they change simutaneously at 9 a.m.

Wonderful questions. i was thinking on this topic from last one week. great work

its useful thank you

How to solve problems like this:
What is the smallest number which leaves remainders 1 and 2 when divided by 7 and 8, respectively.

What is the smallest number which leaves remainders 2 and 12 when divided by 16 and 18, respectively? I understand the answer (66), but I’m looking for a systemetic method to solve this kind of question (when the difference of the divisor and respective remainder is not the same).


Thanx ms sia, ur sums helped me alot !!!

lol the light house sum is in my book and ik that one šŸ˜›

yr site is helpfull but the word problems which i wanted were not there .i wanted word problems like the lighth house ones .whish i find it write now .

sum of two numbers is 60 and their lcm is 175. find their hcf

Can I get some help on area Perimeter and volume sums. Otherwise your this page is wonderful for clearing the concept.

I need Word Problems urgently…I hav 2 tak ’em tomorrow to class…Can any1 help…?
I’ll be thankful =D


Ms. Sia

You did not answer my question asked long back (28 July 2011).

What is the smallest number which leaves remainders 2 and 12 when divided by 16 and 18, respectively? I understand the answer (66), but Iā€™m looking for a systemetic method to solve this kind of question (when the difference of the divisor and respective remainder is not the same).

fnd the greatest number that will divide 43,91,183 so as to leave the same remainder in each case

I need clear explanation for the above problem.please explain

plz help me to solve this problm
a room is 10m 8cm long and 7m 80cm broad. it is to be paved with square tiles of the same size. find the least possible number of such tiles.

Trial and error will be a suitable method. Work with multiples of 7 then add 1, and multiples of 8 then add 2. The common number in both scenarios will be your answer.

i want to know that when we find h.c.f. When word greatest is used then why we take l.c.m. When we find greatest n digit no. Which when divided by x y z leaves remainders a b c

Plz help me solve this
Q. Virginia has two frnds who regularly go round to her house to play. Joan goes round once every 4 days and india goes round every 5 days. How often r both friends at virginia house together.

Cn u pls hlp me in finding the solution for the below problem?
Find the smallest number that is divisible by all even numbers between 5 and 13?

hi could you explain tome in a more detailed way of when to use hcf when to use lcm…….my test is this week

I think answer of the first question is wrong. Could not understand how is the answer 142

its very useful for my daughter thank…..

can you provide the answer key pls? thanks

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