# GCD: Problem Set and Answer

**Math Problem Set**

1. Sam was buying hot dogs and hot dog buns for a backyard barbeque. Hot Dogs come in packs of 16, but buns come in packs of 12. How many packs of each will Sam have to buy so that there are no hot dogs or buns left over?

2. A florist has 72 roses, 84 tulips and 48 orchids that she wants to use to create bouquets. What is the largest number of identical bouquets she can put together without having any owers left over?

3. Three alarm clocks are set o at the same time. If the rst one beeps every 9

seconds, the second one beeps every 12 seconds and the third one beeps every 15 seconds, how long will it be until they beep at the same time?

4. Vince has three pieces of rope with lengths of 300 cm, 312 cm and 396 cm. He wants to cut the three pieces of rope into smaller pieces of equal length with none left over.

(a) What is the greatest possible length of each of the smaller pieces of rope?

(b) How many of the smaller pieces of rope will he have altogether?

5. Two flashing signs are turned on at the same time. One sign flashes every 4

seconds and the other flashes every 6 seconds. How many times will they

flash at the same time in 1 minute?

6. Valerie is cutting a huge block of cheese into smaller cubes for her kids’ snack time. If the block of cheese measures 15 cm by 30 cm by 42 cm and each cube of cheese has a whole number of centimetres as a side length, what is the size of the largest cubes she can cut the block into so there is no leftover cheese?

7. Joe lists the following fractions: 1/56; 2/56; …. 55/56;56/56

He then crosses out any of them that are not in lowest form. How many fractions are left uncrossed once he is done?

8. (a) When is the least common multiple of two numbers a and b equal to axb?

(b) When is the least common multiple of two numbers a and b equal to either

a or b?

9. The gcd of two numbers is 30, and the lcm is 840. If one of the numbers is 120, what is the other number?

10. If a number a is a factor of b and a factor of c, is a a factor of b + c? Explain.

**Answer:**

1. 3 packs of hot dogs and 4 packs of buns

2. 12 bouquets each consisting of 6 roses, 7 tulips, and 4 orchids

3. 180 seconds

4. (a) 12 cm

(b) 84 smaller pieces of rope

5. 5 times

6. 3 cm x 3 cm x 3 cm

7. 24

8. (a) when gcd(a; b) = 1

(b) when a divides b or b divides a

9. 210

10. Yes.

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