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Question (21)

QN0036492

The product of two positive integers is 3600 and their HCF is 20. Their LCM is:

(A) 90
(B) 120
(C) 180
(D) 240

Correct Answer: C

Explanation:

LCM = Product/HCF = 3600/20 = 180.

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Question (22)

QN0036493

Two numbers are in the ratio 3:5 and their HCF is 7. Their LCM is:

(A) 35
(B) 70
(C) 105
(D) 210

Correct Answer: C

Explanation:

The numbers are 21 and 35. Their LCM is 105.

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Question (23)

QN0036494

The smallest positive integer that is divisible by 8, 12 and 15 is:

(A) 60
(B) 90
(C) 120
(D) 180

Correct Answer: C

Explanation:

8 = 2³, 12 = 2² × 3 and 15 = 3 × 5. Hence LCM = 2³ × 3 × 5 = 120.

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Question (24)

QN0036495

The HCF of 72, 108 and 180 is:

(A) 12
(B) 18
(C) 24
(D) 36

Correct Answer: D

Explanation:

72 = 2³ × 3², 108 = 2² × 3³ and 180 = 2² × 3² × 5. Therefore, HCF = 2² × 3² = 36.

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Question (25)

QN0036496

A number N = 2ᵃ3ᵇ5ᶜ is divisible by 180 but not by 360. Which condition could be true?

(A) a = 1, b = 2, c = 1
(B) a = 2, b = 2, c = 1
(C) a = 3, b = 2, c = 1
(D) a = 4, b = 1, c = 1

Correct Answer: B

Explanation:

180 = 2² × 3² × 5, while 360 = 2³ × 3² × 5. Thus a = 2, b ≥ 2 and c ≥ 1.

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Question (26)

QN0036497

Which of the following numbers cannot be a perfect square?

(A) 2⁴ × 3²
(B) , the exponent of 2 is 3.
(C) 2⁶ × 5⁴
(D) 3⁴ × 7²

Correct Answer: B

Explanation:

In a perfect square, the exponent of every prime factor must be even. In option (b), the exponent of 2 is 3.

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Question (27)

QN0036498

The smallest number by which 72 must be multiplied to make it a perfect square is:

(A) 2
(B) 3
(C) 6
(D) 8

Correct Answer: A

Explanation:

72 = 2³ × 3². Multiplying by 2 gives 2⁴ × 3² = 144 = 12².

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Question (28)

QN0036499

The smallest number by which 540 must be divided to obtain a perfect square is:

(A) 5
(B) 10
(C) 15
(D) 20

Correct Answer: C

Explanation:

540 = 2² × 3³ × 5. Dividing by 15 gives 36 = 6².

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Question (29)

QN0036500

If n = 2⁴ × 3³ × 5², the smallest positive integer by which n must be multiplied to make it a perfect square is:

(A) 2
(B) 3
(C) 5
(D) 15

Correct Answer: B

Explanation:

Only the exponent of 3 is odd. Multiplying by 3 changes its exponent from 3 to 4.

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Question (30)

QN0036501

The number 6ⁿ can end with digit 0 for:

(A) every natural number n
(B) n = 1 only
(C) no natural number n
(D) all even values of n

Correct Answer: C

Explanation:

6ⁿ = 2ⁿ × 3ⁿ, so its prime factorisation never contains 5. Hence it cannot be divisible by 10.

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Question (21)

The product of two positive integers is 3600 and their HCF is 20. Their LCM is:

Explanation:

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Question (22)

Two numbers are in the ratio 3:5 and their HCF is 7. Their LCM is:

Explanation:

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Question (23)

The smallest positive integer that is divisible by 8, 12 and 15 is:

Explanation:

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Question (24)

The HCF of 72, 108 and 180 is:

Explanation:

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Question (25)

A number N = 2ᵃ3ᵇ5ᶜ is divisible by 180 but not by 360. Which condition could be true?

Explanation:

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Question (26)

Which of the following numbers cannot be a perfect square?

Explanation:

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Question (27)

The smallest number by which 72 must be multiplied to make it a perfect square is:

Explanation:

Link:

Question (28)

The smallest number by which 540 must be divided to obtain a perfect square is:

Explanation:

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Question (29)

If n = 2⁴ × 3³ × 5², the smallest positive integer by which n must be multiplied to make it a perfect square is:

Explanation:

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Question (30)

The number 6ⁿ can end with digit 0 for:

Explanation:

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