Week 1 Review: Practice Exercises and Problems

Below are the practice exercises for the Week 1 Review on LCM and GCD. You can read the answers and solutions to these exercises and problems.

Practice Exercises

I. Find the GCD of each of the following.
a.) 6, 10
b.) 18, 42
c.) 12, 48, 60
d.) 56, 72
e.) 225, 75

II. Find the LCM of each of the following.

a.) 3, 4
b.) 2, 5
c.) 3, 6, 8
d.) 3, 4, 5
e.) 6, 12, 15

III. Practice Problems

1.) The fractions 1/3, 1/4 and 1/8 are added. To add them, you need to convert them to similar fractions. What will be the least possible denominator of these similar fractions?

2.) In a disco, the red lights blink every 3 seconds and the blues light blink every 5 seconds. The two lights blink every ___ seconds.

3.) Anna, Karen, and Nina go to the same gym. Anna goes every 2 days, Karen goes every 3 days, and Nina goes every 7 days. On June 1, all of them were seen on the gym. What is the soonest date that they will be seen on the gym on same day?

4.) Consider the following sequences:
Sequence 1: 4, 8, 12, 16, 20, 24, …
Sequence 2: 6, 12, 18, 24, …
Notice that 12 and 24 are the first and second common numbers, respectively, to both sequences.
What is the 10th common number?

5.) In Senior High School athletic meet, there are 24 students from Grade 11 and 30 students from Grade 12. Groups are formed such that in each group should have an equal number students from each Grade level.
(a) If everyone is included, how many of such groups can be formed?
(b) When the largest number of groups is formed, how many students from each Grade level are there in one group?

6.) Reduce 42/56 to lowest terms.

7.) Boxes of chocolates have a height of 6 cm each. Boxes of cookies have a height of 8 cm each. A combination of these boxes will be packed in a large box. What should be the minimum height of the large box so that the smaller boxes would exactly fit?

8.) Square cardboard of the same size are to completely cover a rectangle with dimensions 18 cm by 12 What should be the dimensions of the largest possible squares so that there is no wasted cardboard?

9.) Cubes of the same size are to be placed inside a rectangular box. What is the size of the largest possible cubes that can fit exactly inside the box if its dimensions are 21 cm by 35 cm by 84 cm and no space is to be wasted?

10.) In a flour shop, a cake flour comes in 5-kg packages, a pastry flour comes in 3-kg packages and the bread flour comes in 6 kg packages. If Gina bought the same number of kilograms of these flour, what is the minimum number of kilograms of each she must have bought?

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