1. What is the prime factorisation of 12?
- A2² x 3
- B2 x 3²
- C2 x 3
- D2³ x 3
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Answer: A) 2² x 3
12 = 2 x 6 = 2 x 2 x 3 = 2² x 3.
Class 10 Fundamental Theorem of Arithmetic — practice questions with answers
Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. The LCM of 12 and 18 is:
- A36
- B6
- C72
- D54
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Answer: A) 36
12 = 2² x 3, 18 = 2 x 3². LCM = 2² x 3² = 36.
3. The number 2³ x 3 x 5² equals:
- A600
- B1200
- C540
- D660
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Answer: A) 600
2³ = 8, 5² = 25; 8 x 3 x 25 = 24 x 25 = 600.
4. Find the smallest number which when divided by 15, 20 and 25 leaves no remainder.
- A300
- B600
- C330
- D270
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Answer: A) 300
Smallest such number = LCM(15, 20, 25). 15 = 3 x 5, 20 = 2² x 5, 25 = 5². LCM = 2² x 3 x 5² = 300.
5. Four numbers are 2² x 3 x 5, 2 x 3² x 5, 2³ x 3 x 5² and 2² x 3² x 5.
If X is their HCF and Y is their LCM, find the value of .
If X is their HCF and Y is their LCM, find the value of .
- A66
- B54
- C120
- D60
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Answer: D) 60
HCF X uses the lowest powers: 2¹ x 3¹ x 5¹ = 30. LCM Y uses the highest powers: 2³ x 3² x 5² = 8 x 9 x 25 = 1800. = 60.
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