Factors and Multiples Word Problems
Solve each word problem by finding HCF or LCM.
1. Pencils come in packages of 10. Erasers come in packages of 12. Phillip wants
to purchase the smallest number of pencils and erasers so that he will have
exactly 1 eraser per pencil. How many packages of pencils and erasers should
Phillip buy?
2. Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in
plastic containers for her friends at school. She wants to divide the cookies into
identical containers so that each container has the same number of each kind of
cookie. If she wants each container to have the greatest number of cookies
possible, how many plastic containers does she need?
3. Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches
tall. What is the shortest height at which the two stacks will be the same height?
4. Beginning at 8:30 A.M., tours of the National Capitol and the White House begin
at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for
the White House leave every 20 minutes. How often do the tours leave at the
same time?
5. Two neon lights are turned on at the same time. One blinks every 4 seconds and
the other blinks every 6 seconds. In 60 seconds, how many times will they blink
at the same time?
6. The table below shows the number of students in the school choir.
School Choir
Students Number
Girls
48
Boys
64
The choir teacher plans to arrange the students in equal rows. Only girls or boys
will be in each row. What is the greatest number of students that could be in
each row?
7. At a display booth at an amusement park, every visitor gets a gift bag. Some of
the bags have items in them as shown in the table below.
Items in the Gift Bags
Items
Bags
Hat
Every 2nd visitor
T-shirt
Every 7th visitor
Backpack Every 10th visitor
How often will a bag contain all three items?
8. Bridget has swimming lessons every fifth day and diving lessons every third day.
If she had a swimming lesson and a diving lesson on May 5, when will be the
next date on which she has both swimming and diving lessons?
9. Find the greatest number which divides 1628, 1736 and 268 leaving remainders
8,11 and 13 respectively.
10. The length and breadth of the floor of a room is 9m and 6m which is to be paved
with marble square stone tiles of size 75cm.Find the least number of square tiles
required.
11. Can two numbers have 25 as their HCF and 2032 as their LCM? Give reason for
your answer
12. Find the least number of five digits which on dividing by 15, 20, 25, 30 and 35
leaves a remainder of 7 in each case
13. Given that HCF of two numbers is 13 and their product is 9126, determine the
LCM
14. In a school there are 108,162 and 270 students in grades 6, 7 and 8 .All of them
are to be taken on a picnic on a certain day. Find the least number of buses
required such that each bus will take the largest but equal number of students
from each class.
15. There are 45 girls and 36 boys who want to participate in a competition. If each
team must have the same number of girls and the same number of boys,
a. What is the greatest number of teams that can participate
b. How many girls and boys will be on each team?
16. Reduce 216/384 to lowest term using HCF
17. What is HCF of
a. two consecutive numbers
b. two prime numbers
18. Three pieces of wood measuring 35cm, 49cm and 63 cm long have to be divided
into planks of equal length. What is the greatest possible length of each plank?
19. HCF of two numbers is 105. If the two numbers are 525 and 945, find their LCM
20. Find the L.C.M of 2/5, 3/10 and 6/25
21. A merchant has three different types of milk- 324 L, 351 Land 459 L. Find the
minimum number of casks of equal size that can store the milk without mixing.
22. The traffic lights at three different road crossings change after every 24 sec., 36
sec. and 72 sec. respectively. If they all change simultaneously at 8 : 20 : 00 hrs;
then when will they again change simultaneously ?
23. Determine the two numbers nearest to 400 which are exactly divisible by 3,4,5
and 6.
24. Two tanks have capacities of 1020 and 1190 litres respectively. Find the largest
capacity of the container that can be used to fill the tanks.
25. Four children step off together while going to school. Their steps measure 28 cm,
32 cm. 36 cm and 48cm respectively. At what distance from the starting point will
they step off together again?