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Playing With Numbers - 25

Description: Playing with Numbers - 25
Number of Questions: 25
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Tags: Playing with Numbers - 25 Playing with Numbers L.C.M. and H.C.F.
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Which of the following sets of the numbers will have the highest common factor equal to 18?

  1. 38, 58, 124

  2. 36, 54, 126

  3. 28, 54, 126

  4. 36, 54, 128

Show answer
Correct Option: B
Explanation:

36, 54, 126 Factors of 36 = 2 × 2 × 3 × 3 Factors of 54 = 2 × 3 × 3 × 3 Factors of 126 = 2 × 3 × 3 × 7 HCF = 2 × 3 × 3 = 18

Which of the following sets of the numbers will have the LCM equal to 72?

  1. 14, 12, 18

  2. 16, 12, 14

  3. 12, 18, 24

  4. 18, 24, 28

Show answer
Correct Option: C
Explanation:

12, 18, 24 Multiples of 12 = 12, 24, 36, 48, 60, 72, 84 Multiples of 18 = 18, 36, 54, 72, 90 Multiples of 24 = 24, 48, 72, 96 LCM of 12, 18, 24 = 72

Find the LCM of (a + b)2 and (a + b).

  1. (a + b)

  2. (a + b)2

  3. (a + b)3

  4. a - b

Show answer
Correct Option: B

Which of the following sets of numbers will have LCM equal to 300?

  1. 85 and 90

  2. 75 and 60

  3. 60 and 95

  4. 76 and 62

Show answer
Correct Option: B
Explanation:

75 and 60 Factors of 75 = 75, 150, 225, 300, 375 Factors of 60 = 60, 120, 180, 240, 300, 360 LCM of 60 and 75 = 300

What is the LCM of pq (p - q) and pqr (p - q)?

  1. (p - q)

  2. pqr

  3. pqr(p - q)

  4. pq(p - q)

Show answer
Correct Option: C
Explanation:

Factors of pq (p - q) = p × q × (p - q) Factors of pqr (p - q) = p × q × r × (p - q) LCM = p × q × r (p - q)

What is the LCM of x2 - z2 and x + z?

  1. (x + z) (x - z)

  2. (x + z)2

  3. (x - z)2

  4. x - z

Show answer
Correct Option: A
Explanation:

Factors of (x2 - z2) = (x + z) (x - z) Factors of (x + z) = (x + z) LCM = (x + z) (x - z) = (x2 - z2)

Which of the following sets of numbers will have the LCM equal to 105?

  1. 15 and 27

  2. 27 and 61

  3. 21 and 35

  4. 15 and 21

Show answer
Correct Option: D
Explanation:

15 and 21 Factors of 15 = 3 × 5 Factors of 21 = 3 × 7 LCM = 3 × 5 × 7 = 105

Which of the following sets of numbers will have LCM equal to 672?

  1. 84 and 32

  2. 89 and 35

  3. 84 and 36

  4. 94 and 32

Show answer
Correct Option: A
Explanation:

Factors of 84 = 2 × 2 × 3 × 7 Factors of 32 = 2 × 2 × 2 × 2 × 2 LCM = 2 × 2 × 3 × 7 × 2 × 2 × 2 = 672

Which of the following numbers has the least common multiple as 112?

  1. 16, 18

  2. 14, 16

  3. 12, 14

  4. 16, 20

Show answer
Correct Option: B
Explanation:

14, 16 Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126 Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128 LCM = 112 

What is the least common multiple of p3 + q3 + 3p2q + 3pq2 and p2 - q2?

  1. (p + q)3

  2. p + q

  3. (p + q)3 (p - q)

  4. (p - q)3 p + q

Show answer
Correct Option: C
Explanation:

p3 + q3 + 3p3q = (p + q)3 Factors of (p + q) 3 = (p + q) (p + q) (p + q) Factors of (p2 - q2) = (p - q) (p + q) LCM = (p + q)3 (p - q)

Which of the following sets of numbers will have 84 as LCM?

  1. 26, 24, 18

  2. 28, 14, 21

  3. 18, 34, 21

  4. 28, 34, 16

Show answer
Correct Option: B
Explanation:

Multiples of 28 = 28, 56, 84 Multiples of 14 = 14, 28, 42, 56, 70, 84, 98 Multiples of 21 = 21, 42, 63, 84   LCM = 84

Which of the following sets of numbers will have 80y2x as LCM?

  1. 4y2, 16x, 8y

  2. 2y2, 16xy, 8a

  3. 8y2, 16xy, 10y

  4. 18y2, 16xy, 4y

Show answer
Correct Option: C
Explanation:

8y2, 16xy, 10y Factors of 8y2 = 2 × 2 × 2 × y × y Factors of 10y = 2 x 5 x y Factors of 16 × y = 2 × 2 × 2 × 2 × x × y LCM = 2 × 2 × 2 × 2 × 5 x x × y = 80xy2

Which of the following sets of numbers have 140ab as LCM?

  1. 10ab, 20ab, 28ab

  2. 11ab, 21ab, 28ab

  3. 12ab, 20ab, 14ab

  4. 20ab, 26ab, 14ab

Show answer
Correct Option: A
Explanation:

10ab, 20ab, 28ab Factors of 10ab = 2 × 5 × a × b Factors of 20ab = 2 × 2 × 5 × a × b Factors of 28ab = 2 × 2 × 7 × a × b LCM = 140ab

Alex and her three friends go for lunch and find a deal on packages of 6 tacos. He wants to buy the minimum number of packages. So, each gets the same number of tacos and none are left over. How many packages must he buy?

  1. 11

  2. 12

  3. 13

  4. 14

Show answer
Correct Option: B
Explanation:

Number of friends = 4 Number of tacos = 6 LCM of 4 and 6 = 12

Alex can make groups of 3, 4 and 9 pencils with no left over. What is smallest number of pencils Alex needs to make these groups?

  1. 28

  2. 30

  3. 34

  4. 36

Show answer
Correct Option: D
Explanation:

3, 4, 9 Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 Multiples of 9 = 9, 18, 27, 36, 45 LCM of 3, 4, 9 = 36

During summer months, one ice cream truck visits Williams neighbourhood every 4 days and another ice cream truck visits her neighbourhood every 5 days. If both the trucks visited today, when is the next time when both the trucks will visit on the same day?

  1. After 20 days

  2. After 28 days

  3. After 30 days

  4. After 36 days

Show answer
Correct Option: A
Explanation:

4, 5 Multiples of 4 = 4, 8, 12, 16, 20, 24 Multiples of 5 = 5, 10, 15, 20, 25 LCM of 4 and 5 = 20           

Which of the following sets of numbers will have 560b4a as LCM?

  1. 28b, 20ab3, 16b4

  2. 28b, 20ab2, 16b4

  3. 20b2, 28ab, 18b4

  4. 28b4, 18ab3, 16b

Show answer
Correct Option: A
Explanation:

28b2, 20ab3, 16b4 Factors of 28b2 = 2 × 2 × 7 × b × b Factors of 20ab3 = 2 × 2 × 5 × a × b × b × b Factors of 16b4 = 2 x 2 x 2 x 2 x b x b x b x b LCM = 2 × 2 × 7 × 5 × 2 × 2 × b × b × a × b × b = 560ab4

Sam has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How would she cut the strips?

  1. She should cut each piece to be 14 inches wide.

  2. She should cut each piece to be 16 inches wide.

  3. She should cut each piece to be 18 inches wide.

  4. She should cut each piece to be 20 inches wide.

Show answer
Correct Option: C
Explanation:

 HCF of 72 and 90 = 18

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?

  1. 12 minutes

  2. 16 minutes

  3. 20 minutes

  4. 24 minutes

Show answer
Correct Option: D
Explanation:

LCM of 6 and 8: Multiples of 6 = 6, 12, 18, 24, 30 Multiples of 8 = 8, 16, 24, 32 So, LCM of 6 and 8 = 24

Dan exercise every 12 days and Kevin every 8 days. Dan and Kevin both exercised today. How many days will it be until they exercise together again?

  1. They will exercise on the same day after every 24 days.

  2. They will exercise on the same day after every 28 days.

  3. They will exercise on the same day after every 32 days.

  4. They will exercise on the same day after every 40 days.

Show answer
Correct Option: A
Explanation:

 LCM of 12 ans 8 = 24

Rosa is making a game board that is 55 inches by 75 inches. She wants to use square tiles. What is the size of the largest tile she can use?

  1. 4 inches

  2. 5 inches

  3. 7 inches

  4. 10 inches

Show answer
Correct Option: B
Explanation:

55, 75 Factors of 55 = 5 × 11 Factors of 75 = 5 × 5 × 3 HCF = 5

What is the LCM of 22, 54 and 108?

  1. 5442

  2. 2926

  3. 1188

  4. 428

Show answer
Correct Option: C
Explanation:

Factors of 22 = 2 × 11 Factors of 54 = 2 × 3 × 3 × 3 Factors of 108 = 2 × 2 × 3 × 3 × 3 LCM = 2 × 11 × 3 × 3 × 3 × 2 × 3 × 3 × 3 = 1188

The bikers are riding on a circular path. The first rider completes a round in 35 minutes. The second biker complete a round in 25 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

  1. 155

  2. 165

  3. 175

  4. 180

Show answer
Correct Option: C
Explanation:

35, 25 Multiples of 35 = 35, 70, 105, 140,  175, 210 Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200 LCM of 25 and 35 = 175

Cameron is making bead necklace. He has 90 green beads and 108 blue beads. What is the greatest number of identical necklaces he can make if he wants to use all of the beads?

  1. 16

  2. 18

  3. 26

  4. 28

Show answer
Correct Option: B
Explanation:

90, 108 Factors of 90 = 3 × 3 × 2 × 5 Factors of 108 = 2 × 3 × 3 × 2 × 3 HCF = 2 × 3 × 3 = 18

Sharon plants 40 apple trees and 10 peach trees. She wants the same number and type of trees per row. What is the maximum number of trees she can plant per row?

  1. 20

  2. 10

  3. 8

  4. 4

Show answer
Correct Option: B
Explanation:

40, 10 Factors of 40 = 2 × 2 × 2 × 5 Factors of 10 = 2 × 5 HCF = 2 × 5 = 10

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