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SubjectsMathematics
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
Correct answer: C. (2)
Explanation: Step 1: Compare the powers of (2). Step 2: (120=2^3\times3\times5), (180=2^2\times3^2\times5), and (300=2^2\times3\times5^2), so the smallest power is (2). Step 3: HCF uses the smallest power.
Correct answer: C. (3)
Explanation: Step 1: Look at the powers of (5). (48) has no factor (5), (75=3\times5^2), and (125=5^3). Step 2: The highest power of (5) in the LCM is (3). Step 3: A missing prime has power zero, but still compare the existing highest power.
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