HCF AND LCM practice question for Railways, SSC. Review the correct answer and explanation, then continue with related practice below.
If the LCM of the first 110 natural numbers is N, then find the LCM of the first 115 natural numbers.
Correct Answerसही उत्तर
B. 113N / 113N
Explanationव्याख्या
We only need to check the additional numbers 111, 112, 113, 114 and 115.
Here, 111 = 3 × 37, 112 = 2⁴ × 7, 114 = 2 × 3 × 19 and 115 = 5 × 23.
All these required prime factors and powers are already contained in the LCM of the first 110 natural numbers.
However, 113 is a prime number greater than 110, so the factor 113 is not present in N.
Therefore, the new LCM = 113N.
हमें केवल अतिरिक्त संख्याओं 111, 112, 113, 114 और 115 की जाँच करनी है।
यहाँ 111 = 3 × 37, 112 = 2⁴ × 7, 114 = 2 × 3 × 19 और 115 = 5 × 23 हैं।
इनके सभी आवश्यक अभाज्य गुणनखंड और उनकी घातें प्रथम 110 प्राकृतिक संख्याओं के LCM में पहले से मौजूद हैं।
लेकिन 113 एक अभाज्य संख्या है और 110 से बड़ी है, इसलिए 113 का गुणनखंड N में मौजूद नहीं है।
अतः नया LCM = 113N।
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