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LCM and HCF Practice Set

1. The smallest number which is divisible by 12, 16, 18, 21 and 28 after diminished by 7 is:

सबसे छोटी संख्या जिसमे से 7 घटाने के बाद, 12, 16, 18, 21 और 28 द्वारा विभाजित हो जाती है

A. 1008
B. 1015
C. 1022
D. 1032

Answer: Option B
Explanation: Required numbers = (LCM of 12, 16, 18, 21, 28) + 7
= 1008 + 7
= 1015

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2. The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is:

दो नंबरों का HCF 11 है और उनका LCM 7700 है। यदि संख्याओं में से एक 275 है, तो दूसरा है

A. 279
B. 283
C. 308
D. 318

Answer: Option C
Explanation: Other number = [11 × 7700275]
= 308

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3. The product of two numbers is 4107. If the HCF of those numbers is 37, then the greater number is:

दो संख्याओं का गुणनफल 4107 है। यदि उन संख्याओं का HCF 37 है, तो बड़ी संख्या है

A. 101
B. 107
C. 109
D. 111

Answer: Option D
Explanation: Let the numbers be 37a and 37b.
Then, 37a × 37b = 4107
ab = 3
Now, co-primes with product 3 are (1, 3)
So, the required numbers are (37 × 1, 37 × 3)
i.e., (1, 111)
Therefore greater number = 111

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4. The greatest possible length which can be used to measure exactly the length 7m, 3m, 85cm, 12m, 95 cm is:

सबसे बड़ी संभव लंबाई जिसका उपयोग लंबाई 7 मीटर, 3 मीटर, 85 सेमी, 12 मीटर, 95 सेमी मापने के लिए किया जा सकता है

A. 15 cm
B. 25 cm
C. 35 cm
D. 42 cm

Answer: Option C
Explanation: Required length = HCF of 700 cm, 385 cm and 1295 cm
= 35 cm

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5. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remained in each case.

43, 91 और 183 को विभाजित करने वाली सबसे बड़ी संख्या बताएं जिससे प्रत्येक मामले में समान शेष बचे ।

A. 4
B. 7
C. 9
D. 13

Answer: Option A
Explanation: Required number
= HCF of (91 – 43), (183 – 91) and (183 – 43)
= HCF of 48, 92 and 140
= 4

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6. The G.C.D. of 1.08, 0.36 and 0.9 is:

1.08, 0.36 और 0.9 का G.C.D. है:

A. 0.03
B. 0.9
C. 0.18
D. 0.108

Answer: Option C
Explanation: Given numbers are 1.08, 0.36 and 0.90
HCF of 108, 36 and 90 is 18
HCF of given numbers – 0.18

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