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13.Javier's Linens sells hand towels in sets of 10 and bath towels in sets of 5. If the store sold the same number of each this morning, what is the smallest number of each type of towel that the store must have sold?​

Answer» <html><body><p><strong>Step-by-step explanation:</strong></p><h2>Selling hand towels in sets of 10 , the <a href="https://interviewquestions.tuteehub.com/tag/number-582134" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBER">NUMBER</a> of hand towels sold must be a multiple of 10 .</h2><h2>Selling bath towels in sets of <a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a> , the number of hand towels sold must be a multiple of 6 .</h2><h2>If the store sold the same number of each type of towel,</h2><h2>that same number of each type of towel sold must be a multiple of 10 , and 6 .</h2><h2>The smallest possible number of each type of towel sold is the least common multiple (LCM) of 10 , and 6 .</h2><h2>That number is highlight%2830%29 .</h2><h2>Of course, the store may have sold</h2><h2>2%2A30=60 of each type of towel, or</h2><h2>3%2A30=90 , or 4%2A30=120 , or ...</h2><h2></h2><h2>HOW TO FIND THE LCM:</h2><h2>1) We could list the multiples of one of the numbers (preferably the largest).</h2><h2>The multiples of 10 are:</h2><h2>10 , 20 , 30 , 40 , ...</h2><h2>Then we would check then one by one, from smallest to largest,</h2><h2>to see if we can find a multiple of the other number(s).</h2><h2>In this case, 10 , and 20 are not multiples of 6 ,</h2><h2>but 30 is, so 30 is the LCM of 10 , and 6 .</h2><h2>2) Sometimes the method above does not give you the answer fast enough.</h2><h2>A more general method involves finding the prime factorizations.</h2><h2>The prime factorizations of 10 , and 6 are</h2><h2>10=2%2A5 and 6=2%2A3 .</h2><h2>The prime factorization of the LCM <a href="https://interviewquestions.tuteehub.com/tag/includes-1039937" style="font-weight:bold;" target="_blank" title="Click to know more about INCLUDES">INCLUDES</a> all prime <a href="https://interviewquestions.tuteehub.com/tag/factors-458933" style="font-weight:bold;" target="_blank" title="Click to know more about FACTORS">FACTORS</a> found in the numbers, with the greatest exponents (if any).</h2><h2>In this case,</h2><h2>LCM%2810%2C6%29=2%2A3%2A5=30 ,</h2><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><h2>Hope its <a href="https://interviewquestions.tuteehub.com/tag/help-1018089" style="font-weight:bold;" target="_blank" title="Click to know more about HELP">HELP</a>...</h2></body></html>


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