Teacher2Teacher 
Q&A #7499 
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From: MathFreak <saltof_theearth@yahoo.co.in> To: Teacher2Teacher Public Discussion Date: 2004091203:05:00 Subject: Why it works WHY IT WORKS I think it works because the product of two numbers is also the product of the L.C.M and H.C.F. of the two numbers. Say 1/28+ 1/42 LCM of 28 and 42: 28=2^2*3^0* 7^1 42=2^1*3^1*7^1 LCM= 2^2*3^1*7^1=4*3*7=84 HCF=2^1*3^0*7^1=2*1*7=14 HCF*LCM=2^2*2^1*3^1*3^0*7^1*7^1=28*42 Therefore,1/28+1/42= 1/84 *(3+2)=5/84 as also 1/LCM*HCF times (3*HCF+2*HCF)= 1/28*42 times(42+28) Since 3HCF+2HCF=5HCF=5*14=42+28=70. Hope this helps! Mathfreak
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