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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