The smallest number which when diminished by 3 is divisible by 14, 28,

1.	The smallest number which when diminished by 3 is divisible by 14, 28, 36 and 45, is?
Answer» <html><body><p><strong>Answer: 1263 </strong></p><p></p><p>Solution -</p><p></p><p></p><p>Here, at <a href="https://interviewquestions.tuteehub.com/tag/first-461760" style="font-weight:bold;" target="_blank" title="Click to know more about FIRST">FIRST</a> we have to find the prime factorisation of the <a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> numbers</p><p></p><p></p><p>Prime Factors of 14 = <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> × 7</p><p></p><p>Prime Factors of 28 = 2 × 2 × 7</p><p></p><p>Prime Factors of 36 = 2 × 2 × 3 × 3</p><p></p><p>Prime Factors of 45 = 3 × 3 × <a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a></p><p></p><p>∴ LCM of 14, 28, 36 & 45</p><p></p><p>= 2 × 2 × 3 × 3 × 5 × 7</p><p></p><p>= 1260</p><p>∴ <a href="https://interviewquestions.tuteehub.com/tag/required-1185621" style="font-weight:bold;" target="_blank" title="Click to know more about REQUIRED">REQUIRED</a> smallest number = 1260 + 3</p><p></p><p>= 1263</p><p>The required smallest number is 1263</p></body></html>

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