Two numbers have HCF 11 and LCM 1694, and both numbers lie between 100 and 200.
Which pair is it?

Write the numbers as $11a$ and $11b$ with a, $b$ co-prime; LCM = $11ab=1694$ gives $ab=154=2\times 7\times$ 11. For both numbers to lie between 100 and 200, a and $b$ must lie between 10 and 18, and (a, b) = (11, 14) works, giving 121 and 154. The pair 11 and 1694 does have HCF 11 and LCM 1694 but lies outside the stated range; 132 and 143 give LCM 1716; 110 and 154 give HCF 22, not 11.