Word Problems
HCF
A florist has 36 roses, 27 tulips, and 18
carnations she must use to create
bouquets. What is the largest number of
bouquets she can make without having
any flowers left over?
The HCF is the number we're looking
for, the remaining factors in each
number tell us how may of each to
put in each bouquet.
• roses:
36 = 22 x 32
• tulips:
27 = 33
• carnations:
18 = 32
HCF = 32 = 9 bouquets (smallest
exponent of 3 is 2)
each bouquet will have
• roses:
36 : 9 = 4
• tulips:
27 : 9 = 3
• carnations: 18 : 9 = 2
Say you have 60 pencils, 90 pens and
120 books and you want to make
packages of pencils, pens and books to
donate to your school for students who
cannot afford these supplies. What is
the maximum number of packages you
can make using all items, and how
many pencils, pens and books will be in
each package?
• pencils: 22 x 3 x 5
• pens: 2 x 32 x 5
• books: 23 x 3 x 5
• HCF
= 2 x 3 x 5 = 30 packages
content of each package 
• Pencils = 60 : 30 = 2 pencils
• Pens
= 90 : 30 = 3 pens
• Books = 120 : 30
= 4 books
• Each package with 2 pencils, 3 pens, and
4 books in each package.
Try this!
Dean 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?
LCM
You and your three friends go to
lunch and find a deal on packages of
6 tacos. You want to buy the
minimum number of packages so
you each get the same number of
tacos and none are left over. How
many packages must you buy?
the LCM of 4 and 6?
4 = 22
6=2x3
LCM = 22 x 3 = 12.
12 tacos requires 2 packages and you
each will get 3 tacos.
One trip around a running track is
440 yards. One jogger
can complete one lap in 8 minutes,
the other can complete it in 6
minutes. How long will it take for
both joggers to arrive at their
starting point together if they start
at the same time and maintain
their jogging pace?
LCM of 6 and 8?
6=2x3
8 = 23
LCM = 23 x 3 = 24 minutes
• the slower jogger will have
completed 3 laps
( 24 : 8 = 3)
• the faster jogger will have
completed 4 laps
( 24 : 6 = 4)
Try this!
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?
Is it a HCF or LCM word problems?
Frank is buying Hot Dogs for a
class picnic. Hot dogs are sold in
pckgs of 10. Hot Dog buns are
sold in pckgs of 8. What is the
smallest number of hot dogs and
buns Frank can buy to have an
equal number of each?
You are making pumpkin pies for
the bake sale. Piecrusts are sold
in pckgs of 3. Pie filling is sold in
4-can pckgs. What is the least
number of piecrusts and filling that
you can buy to have the same
number of each?
Thrift market sells apple juice in 8oz
containers, pineapple juice in 12 oz
containers and grape juice in 16 oz
containers. If Mark wants to have
the same amount of each juice to
make some punch, what is the least
amount of ounces he should buy of
each flavor of fruit juice?
Mr. Brackett works in factory with
his two sons. He is really happy
with his job because he gets to
spend some time with his beloved
sons not only at home but also at
work! He is allowed to take a
break every 140 minutes while his
two sons are allowed to take
breaks in 210 minutes and 280
minutes. How many minutes will
they have to wait after their first
break together to get together
again?
Mrs.Flynn has baked 84 raisin
cookies, 106 muffins and 128
chocolate chip cookies, which all
smell delicious! They smell so good
she would like to keep 4 raisin
cookies, 6 muffins and 8 chocolate
chip cookies for herself though she
know she has to cut down on
sweets. She'll then put the rest into
boxes with equal numbers of each
type. What would be the largest
number of cookies or muffins in
each box?