Name: ________________
Math 7 accel.
Worksheet: GCF & LCM Practice Problems
Oct. 25, 2011
Find the GCF of the following sets of numbers.
1.) 90 and 144
2.) 90, 54 and 60
3.) 180, 342 and 378
4.) 378, 972, and 1134
Find the GCF of the following monomials.
5.) 9𝑥 2 𝑦 and 21𝑥𝑦
6.) 42𝑎3 𝑏 4 and 70𝑎4 𝑏 3
State whether the following pairs of monomials are relatively prime. If not, find the GCF.
7.) 16, 25
8.) 7, 49
9.) 17xy2, 24y
11.) 51ac, 33b
12.) Decide whether the expressions 3(𝑚 + 𝑛) and 5(𝑚 + 𝑛) are relatively prime. If
they are not, what is their GCF?
Find the LCM of the following sets of numbers.
14.) 6, 9 and 12
15.) 18 and 54
16.) 8, 14 and 35
17.) 180, 144 and 108
Find the LCM of the following sets of monomials.
18.) 3𝑎𝑏, 6𝑎, and 8𝑏 2
20.) 2𝑥, 5𝑦, and 7𝑧
19.) 𝑚𝑛2 , 2𝑛3 , and 4𝑚2 𝑛2
21.) Blanche has 60 roses, 105 tulips, and 120 daisies with which to make flower
arrangements. What is the largest number of identical arrangements that she can make
using all of the flowers? How many of each flower type will be in each arrangement?
22.) Three pieces of timber have lengths of 102 ft., 68 feet, and 85 ft. Matt, who is a
sawmill operator, needs to cut the timber into logs of equal length. What is the greatest
possible length that the logs can be cut, without any leftovers? How many logs of this
length will result?
23.) Emily is catering a party and is responsible for preparing and doling out appetizers
onto individual plates. She has 48 mini quiches, 64 chicken wings, 80 cheese puffs, and
112 bread sticks. She wants every kind of food on each plate, and she wants to distribute
the food evenly. She also does not want any food to be left over. What is the largest
number of plates she can fill? How many of each appetizer should she put on each plate?
24.) Edward, Paul, and Jack are at the go-kart track. Jack’s go-kart takes exactly 3
minutes to complete a lap. Paul’s go-kart takes exactly 4 minutes, and Edward’s takes
exactly 5 minutes. If they all leave the start/finish line at the same time, how long will it
be before they are alongside each other at the start/finish line again? How many laps will
each have completed at that time?
25.) Daisy puts out her recycling once a week, takes her trash out every 3 days, and
sweeps her front porch every other day. If she does all three on a Monday, how many
days will it be before she does all three again on the same day? What day of the week
will it be then?
26.) Explain how you can easily find the LCM for a set of numbers that is relatively
prime.