allery1 ରୁ 10 ପର୍ଯ୍ୟନ୍ତ ପ୍ରତ୍ୟେକ ସଂଖ୍ୟା ଦ୍ୱାରା ବିଭାଜ୍ୟ କ୍ଷୁଦ୍ରତମ ସଂଖ୍ୟାଟି ହେଉଛି:
A1260
B5040
C3600
D2520
Answer & Solution
Correct answer: D. 2520
1. ଏହିପରି କ୍ଷୁଦ୍ରତମ ସଂଖ୍ୟାଟି ହେଉଛି 1 ରୁ 10 ପର୍ଯ୍ୟନ୍ତ ସଂଖ୍ୟାଗୁଡ଼ିକର LCM।
2. 10 ପର୍ଯ୍ୟନ୍ତ ପ୍ରତ୍ୟେକ ମୌଳିକ ସଂଖ୍ୟାର ସର୍ବୋଚ୍ଚ ଘାତ ନିଅନ୍ତୁ: 8 ରୁ 2^3, 9 ରୁ 3^2, ତା'ପରେ 5 ଏବଂ 7।
3. ତେଣୁ LCM = 8 x 9 x 5 x 7।
4. ତାହା ହେଉଛି 72 x 35 = 2520।
5. 1260 ସଂଖ୍ୟାଟି 8 ଦ୍ୱାରା ବିଭାଜ୍ୟ ନୁହେଁ, ଏବଂ 5040 ଓ 3600 ଆବଶ୍ୟକତାଠାରୁ ବଡ଼, ତେଣୁ କେବଳ 2520 ହିଁ କ୍ଷୁଦ୍ରତମ।
_Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_
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