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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" ><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" ><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" ><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" ><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" ><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" ><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" ><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" ><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" ><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" ><strong>Areas</strong></a></TR><br><TR><a href="volume.html"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" ><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" ><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" ><strong>Clocks</strong></a></TR><br><TR><a href="" ><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" ><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" ><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" ><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><font size="5"><center><b>H.C.F AND L.C.M</b></center></font><br><br><br><br><pre><font size=4><strong><u>Facts And Formulae:</u></strong></font> <font size=4>1.Highest Common Factor:(H.C.F) or Greatest Common Meaure(G.C.M) :<br> The H.C.F of two or more than two numbers <br>is the greatest <br>number that divides each of them exactly.<br><strong><u>There are two methods <u></u></u>:<strong></strong></strong>1.<strong><u>Factorization method:</u></strong> Express each one<br> of the given numbers as the product of prime<br> factors.<br> The product of least powers of common prime factors gives HCF.<br><br>Example : Find HCF of 2<sup>6</sup> * 3<sup>2</sup>*5*7<sup>4</sup> , 2<sup>2</sup> *3<sup>5</sup>*5<sup>2</sup> * 7<sup>6</sup> , 2*5<sup>2</sup> *7<sup>2</sup><br>Sol: The prime numbers given common numbers are 2,5,7<br>Therefore HCF is 2<sup>2</sup> * 5 *7<sup>2</sup> .<br><br><br><br>2.<strong><u>Division Method</u></strong> : Divide the larger number by<br> smaller one. Now divide the divisor by<br> remainder. Repeat the process<br> of dividing preceding number last obtained till<br> zero is obtained as <br>number. The last divisor is HCF.<br> Example: Find HCF of 513, 1134, 1215<br>Sol: <br><br><pre> 1134) 1215(1 1134 ---------- 81)1134(14 81 ----------- 324 324 ----------- 0 ----------- HCF of this two numbers is 81. 81)513(6 486 -------- 27)81(3 81 ----- 0 ---</pre><br>HCF of 81 and 513 is 27.<br><br><br><br>3.Least common multiple[LCM] : The least number which is <br>divisible by each one of given<br> numbers is LCM.<br><strong><u>There are two methods for this:</u></strong><br><br>1.<strong><u>Factorization method</u></strong> :<br><br> Resolve each one into product of prime factors.<br> Then LCM is product of highest powers <br>of all factors.<br><br>2.Common division method.<br><strong><u>Problems:</u></strong><br><br>1.The HCF of 2 numbers is 11 and LCM is 693.If one <br>of numbers is 77.find other.<br>Sol: Other number = 11 * 693/77=99.<br><br><br><br>2.Find largest number of 4 digits divisible by 12,15,18,27<br>Sol: The largest number is 9999.<br>LCM of 12,15,18,27 is 540.<br>on dividing 9999 by 540 we get 279 as remainder.<br>Therefore <br>number =9999 鈥?? 快捷鍵說明
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