SOLUTION: The number 77 is divided into two parts such that H.C.F of two parts is 11 and their L.C.M is 110. The smaller of the two parts is

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Question 890460: The number 77 is divided into two parts such that H.C.F of two parts is 11 and their L.C.M is 110. The smaller of the two parts is
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The number 77 is divided into two parts such that H.C.F of two parts is 11 and their L.C.M is 110. The smaller of the two parts is

Let smaller number be S
Then larger number = 77 – S
The product of the GCF and the LCM is 1,210 (11 * 110)
Since the product of the GCF and LCM of ANY 2 numbers, equals the product of the 2 numbers, then we can say that:
1,210 = S(77 - S), or S(77 – S) = 1,210


(S – 22)(S – 55) = 0
S, or smaller number = OR S = 55 (ignore, as this CANNOT be smaller #)
You can do the check!!
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