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Playing With Numbers - 20

Description: Playing with Numbers - 20
Number of Questions: 25
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Tags: Playing with Numbers - 20 Playing with Numbers L.C.M. and H.C.F. Rounding-off Rule
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What is the LCM of 18 and 7?

  1. 18

  2. 112

  3. 126

  4. 128

Show answer
Correct Option: C
Explanation:

Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, ... Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, ... LCM = 126

What is the HCF of 24 and 16?

  1. 8

  2. 16

  3. 24

  4. 32

Show answer
Correct Option: A
Explanation:

Prime factorisation of 24 = 2 × 2 × 2 × 3 Prime factorisation of 16 = 2 × 2 × 2 × 2 HCF of 24 and 16 = 2 × 2 × 2 = 8

What is the LCM of 1 and 2?

  1. 1

  2. 2

  3. 4

  4. 6

Show answer
Correct Option: B
Explanation:

Multiples of 1 = 1, 2, 3, ... Multiples of 2 = 2, 4, ... LCM of 1 and 2 = 2

What is the HCF of 56 and 40?

  1. 6

  2. 8

  3. 10

  4. 19

Show answer
Correct Option: B
Explanation:

Prime factorisation of 56 = 2 × 2 × 2 × 7 Prime factorisation of 40 = 2 × 2 × 2 × 5 HCF of 56 and 40 = 2 × 2 × 2 = 8

What is the highest common factor of 16 and 32?

  1. 2

  2. 3

  3. 4

  4. 16

Show answer
Correct Option: D
Explanation:

Prime factorisation of 16 = 2 × 2 × 2 × 2 Prime factorisation of 32 = 2 × 2 × 2 × 2 × 2 HCF of 16 and 32 = 2 × 2 × 2 × 2 = 16

Which of the following is the highest common factor of 21 and 56?

  1. 1

  2. 3

  3. 7

  4. 9

Show answer
Correct Option: C
Explanation:

Prime factorisation of 21 = 3 × 7 Prime factorisation of 56 = 2 × 2 × 2 × 7 HCF of 21 and 56 = 7

What is the highest common factor of 39 and 65?

  1. 9

  2. 12

  3. 13

  4. 16

Show answer
Correct Option: C
Explanation:

Prime factorisation of 39 = 3 × 13 Prime factorisation of 65 = 5 × 13 HCF of 39 and 65 = 13

What is the highest common factor of 15 and 25?

  1. 0

  2. 5

  3. 15

  4. 25

Show answer
Correct Option: B
Explanation:

Prime factorisation of 15 = 3 × 5 Prime factorisation of 25 = 5 × 5 HCF of 15 and 25 = 5

Which of the following is the highest common factor of 27 and 9?

  1. 3

  2. 6

  3. 9

  4. 18

Show answer
Correct Option: C
Explanation:

Prime factorisation of 27 = 3 × 3 × 3 Prime factorisation of 9 = 3 × 3 HCF of 27 and 9 = 9

What is the highest common factor of 14 and 70?

  1. 14

  2. 16

  3. 18

  4. 20

Show answer
Correct Option: A
Explanation:

Prime factorisation of 14 = 2 × 7 Prime factorisation of 70 = 2 × 7 × 5 HCF of 14 and 70 = 14

Which of the following is the highest common factor of 51 and 18?

  1. 2

  2. 3

  3. 7

  4. 9

Show answer
Correct Option: B
Explanation:

Prime factorisation of 51 = 3 × 17 Prime factorisationof 18 = 2 × 3 × 3 HCF of 51 and 18 = 3

What is the HCF of 1470 and 220?

  1. 8

  2. 9

  3. 10

  4. 11

Show answer
Correct Option: C
Explanation:

Prime factorisation of 1470 = 2 × 3 × 5 × 7 × 7 Prime factorisation of 220 = 2 × 2 × 5 × 11 HCF of 1470 and 220 = 10

Which of the following is the HCF of 594 and 1265?

  1. 9

  2. 11

  3. 13

  4. 15

Show answer
Correct Option: B
Explanation:

Prime factorisation of 594 = 2 × 3 × 3 × 3 × 11 Prime factorisation of 1265 = 5 × 23 × 11 HCF of 594 and 1264 = 11

Which of the following sets of numbers will have the highest common factor equal to 16?

  1. 48, 96, 145

  2. 24, 40, 64

  3. 50, 560, 140

  4. 48, 80, 112

Show answer
Correct Option: D
Explanation:

48, 80, 112 Prime factorisation of 48 = 2 × 2 × 2 × 2 × 3 Prime factorisation of 80 = 2 × 2 × 2 × 2 × 5 Prime factorisation of 112 = 2 × 2 × 2 × 2 × 7 HCF = 2 × 2 × 2 × 2 = 16

Which of the following sets of the numbers has 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 Prime factorisation of 36 = 2 × 2 × 3 × 3 Prime factorisation of 54 = 2 × 3 × 3 × 3 Prime factorisation of 126 = 2 × 3 × 3 × 7 HCF = 2 × 3 × 3 = 18

Which of the following is the highest common factor of 2346 and 6435?

  1. 2

  2. 3

  3. 5

  4. 9

Show answer
Correct Option: B
Explanation:

Prime factorisation of 2346 = 2 × 3 × 391 Prime factorisation of 6435 = 3 × 3 × 5 × 11 × 13 HCF = 3

Which of the following is the highest common factor of 2527 and 18228?

  1. 7

  2. 9

  3. 18

  4. 27

Show answer
Correct Option: A
Explanation:

Prime factorisation of 2527 = 7 × 19 × 19 Prime factorisation of 18228 = 2 × 2 × 3 × 7 × 7 × 31 HCF of 2527 and 18228 = 7

Which of the following sets of the number has 72 as LCM?

  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 and  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
Explanation:

Factors of (a + b)2 = (a + b) × (a + b) Factors of (a + b) = (a + b) LCM = (a + b)2

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)

Which of the following pairs of numbers will have 300 as LCM?

  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 Multiples of 75 = 75, 150, 225, 300, 375, ... Multiplesof 60 = 60, 120, 180, 240, 300, 360, ... LCM of 60 and 75 = 300

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)

Which of the following pairs of number will have 672 as LCM?

  1. 84 and 32

  2. 89 and 35

  3. 84 and 36

  4. 94 and 32

Show answer
Correct Option: A
Explanation:

Prime factorisation of 84 = 2 × 2 × 3 × 7 Prime factorisation of 32 = 2 × 2 × 2 × 2 × 2 LCM = 2 × 2 × 3 × 7 × 2 × 2 × 2 = 672

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 + 3p2q + 3pq2 = (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 pairs of number will have 105 as LCM?

  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 Prime factorisation of 15 = 3 × 5 Prime factorisation of 21 = 3 × 7 LCM = 3 × 5 × 7 = 105

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