# GCF AND LCM WORD PROBLEMS WORKSHEET

1) Lily has collected 8 U.S. stamps and 12 international stamps. She wants to display them in identical groups of U.S. and international stamps, with no stamps left over. What is the greatest number of groups Lily can display them in ?

2) Jill wants to put 45 sunflower plants, 81 corn plants, and 63 tomato plants in her garden. If she puts the same number of plants in each row and if each row has only one type of plant, what is the greatest number of plants Jill can put in one row ?

3) Two numbers are in the ratio 6 : 7 and their greatest common factor (GCF) is 13. Find the numbers.

4) In a clock, a large gear completes a rotation every 45 seconds, and a small gear completes a rotation every 18 seconds. If the gears are aligned now, how many seconds will pass before the gears are aligned again ?

5) Dante is planting his rose garden. He knows he can plant all of his roses by planting 12 or 15 rose bushes in every row. What is the least number of rose bushes Dante could have ?

6) Two numbers are in the ratio 5 : 9. If the second number is 72, find their least common multiple. To make all the groups identical and find the greatest number of groups, we have to find the greatest number which can divide 8 and 12 exactly. That is the greatest common factor of (GCF) of 8 and 12.

GCF (8, 12)  =  4

That is, 8 U.S stamps can be displayed in 4 groups at 2 stamps/group.

And 12 international stamps can be displayed in 4 groups at 3 stamps/group.

In this way, each of the 4 groups would have 2 U.S stamps and 3 international stamps. And all the 4 groups would be identical.

Hence, the greatest number of groups can be made is 4.

To put the same number of plants in each row and if each row has only one type of plant, we have to find the greatest number that can evenly divide 45, 81 and 63. That is the highest common factor of 45, 81 and 63.

GCF (45, 81, 63)  =  9

9 is the greatest number of plants Jill can put in one row.

Because the two numbers are in the ratio 6 : 7, the numbers are assumed to be 6x and 7x.

GCF (6x, 7x)  =  x

But, it is given that GCF of two numbers is 13.

Then,

x  =  13

Substitute 13 for x in 6x and 7x.

6(13)  =  78

7(13)  =  91

The two numbers are 78 and 91.

For example, let the large and small gears complete a rotation every 3 seconds and 4 seconds respectively.

Then the large gear completed rotations in 3, 6, 9, 12 seconds...

Like this, the small gear completes rotations in 4, 8, 12 seconds...

So, if the two gears are aligned now, again they will align in 12 seconds. This 12 seconds is the least common multiple (LCM) of 3 and 4.

The same thing happened in our problem. To find the time pass before the gears align again, we have to find the least common multiple of 45 seconds and 18 seconds. LCM (45, 18)  =  Product of all prime factors

=  3 ⋅ 3 ⋅ 5 ⋅ 2

=  90

90 seconds will pass before the gears are aligned again.

To find the least number of rose bushes, we have to find the least number that is evenly divisible by 12 and 15. That is the least common multiple of 12 and 15.

Find the least common multiple of 12 and 15. LCM (12, 15)  =  Product of all prime factors

=  3 ⋅ 2 ⋅ 2 ⋅ 5

=  60

60 is the least number of rose bushes Dante could have.

Because the two numbers are in the ratio 5 : 7, the numbers are assumed to be 5x and 9x.

But, it is given that the second number is 72.

Then,

9x  =  72

Divide each side by 9.

x  =  8

The first number  =  5(8)  =  40.

Find the least common multiple of 40 and 72. LCM (40, 72)  =  Product of all prime factors

=  2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 3 ⋅ 3

=  360

The least common multiple of the two numbers is 360. Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

WORD PROBLEMS

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and Venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

## Recent Articles 1. ### Linear Growth and Decay

May 22, 22 03:05 AM

Linear Growth and Decay

2. ### Worksheet on Probability

May 22, 22 01:15 AM

Worksheet on Probability