Q. Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what is the other number? (2023)
Solution
Using the relationship LCM = (Product of the numbers) / HCF, we can find the other number: 72 = (16 * x) / 8, leading to x = 24.
Correct Answer:
B
— 24
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Q. What is the HCF of 36, 60, and 48?
Solution
The prime factorization gives: 36 = 2^2 * 3^2, 60 = 2^2 * 3 * 5, 48 = 2^4 * 3. The HCF is 2^2 * 3 = 12.
Correct Answer:
B
— 12
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Q. What is the LCM of 8, 12, and 16?
Solution
The LCM of 8, 12, and 16 is 48, as it is the smallest number that is a multiple of all three.
Correct Answer:
B
— 96
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Q. What is the smallest number that is divisible by both 18 and 24?
Solution
The LCM of 18 and 24 is 72, which is the smallest number divisible by both.
Correct Answer:
A
— 72
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Q. Which of the following numbers is a multiple of both 8 and 12? (2023)
Solution
The LCM of 8 and 12 is 24, which is a multiple of both.
Correct Answer:
A
— 24
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Q. Which of the following pairs of numbers has an HCF of 1? (2023)
-
A.
8 and 12
-
B.
15 and 28
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C.
9 and 27
-
D.
14 and 21
Solution
The HCF of 15 and 28 is 1, making them coprime.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has an HCF of 6? (2023)
-
A.
12 and 18
-
B.
15 and 25
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C.
10 and 20
-
D.
8 and 16
Solution
The HCF of 12 and 18 is 6, as both numbers are divisible by 6, while the other pairs have higher HCFs.
Correct Answer:
A
— 12 and 18
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Q. Which of the following statements is true regarding HCF and LCM? (2023)
-
A.
HCF is always greater than LCM
-
B.
HCF and LCM can be equal
-
C.
HCF is the product of prime factors
-
D.
LCM is always less than HCF
Solution
HCF and LCM can be equal when both numbers are the same.
Correct Answer:
B
— HCF and LCM can be equal
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Q. Which of the following statements is true regarding the HCF and LCM of two numbers? (2023)
-
A.
HCF is always greater than LCM
-
B.
HCF is the product of the numbers
-
C.
LCM is always less than the product of the numbers
-
D.
HCF * LCM = Product of the numbers
Solution
The correct statement is that HCF * LCM = Product of the numbers.
Correct Answer:
D
— HCF * LCM = Product of the numbers
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