Marie Anne de Bourbon, "Légitimée de France" (2 October 1666 – 3 May 1739) was the eldest legitimised daughter ("fille légitimée de France") of King Louis XIV of France and his mistress Louise de La Vallière.
 At the age of thirteen, she was married to Louis Armand de Bourbon, Prince of Conti and as such was the Princess of Conti by marriage.
 Her father's favourite daughter, Marie Anne was widowed in 1685 aged 19.
 She never married again and had no children.
 Following her mother's retirement to a convent, Marie Anne continued to reside at her father's court and was later her mother's heiress.
 She later became the Duchess of La Vallière in her own right.
Philippine Élisabeth d'Orléans known as "Mademoiselle de Beaujolais" (Philippine Élisabeth Charlotte; 18 December 1714 – 21 May 1734) was the daughter of Philippe d'Orléans, duc d'Orléans (Regent from 1715 to 1723) and his wife, Françoise-Marie de Bourbon, the youngest legitimised daughter of King Louis XIV and his mistress, Madame de Montespan.
 As a member of the reigning House of Bourbon, and of the House of Orléans, Philippine Élisabeth was a Princesse du Sang.
 She died of smallpox at the age of nineteen.
Louise Diane d'Orléans (27 June 1716 – 26 September 1736) was the sixth daughter and last child of Philippe d'Orléans, Duke of Orléans ("Regent of the Kingdom" from 1715 to 1723) and his wife, Françoise Marie de Bourbon, the youngest legitimised daughter of King Louis XIV of France and his mistress, Madame de Montespan.
 She was born during the Regency of Philippe d'Orléans, the Regent of Louis XV of France.
 The Princess of Conti by marriage, she died in childbirth at the age of twenty.
 Some sources refer to her as "Louis Diane".
Louise Françoise de Bourbon, "Légitimée de France" (1 June 1673 – 16 June 1743) was the eldest surviving legitimised daughter of Louis XIV of France and his maîtresse-en-titre, Madame de Montespan.
 She was said to have been named after her godmother, Louise de La Vallière, the woman that her mother had replaced as the king's mistress.
 Prior to her marriage, she was known at court as "Mademoiselle de Nantes".
Louis XIV (5 September 16381 September 1715), known as Louis the Great ("Louis le Grand ") or the Sun King ("le Roi Soleil "), was a monarch of the House of Bourbon who reigned as King of France from 1643 until his death in 1715.
 His reign of 72 years and 110 days is the longest recorded of any monarch of a sovereign country in European history.
 In the age of absolutism in Europe, Louis XIV's France was a leader in the growing centralization of power.
Louise Anne de Bourbon, "Mademoiselle de Charolais" (23 June 1695 – 8 April 1758) was a French noblewoman, the daughter of Louis de Bourbon, Prince of Condé.
 Her father was the grandson of "le Grand Condé", while her mother, Louise Françoise de Bourbon, was the eldest surviving legitimised daughter of Louis XIV of France and his "maîtresse-en-titre", Madame de Montespan.
Louise Adélaïde d'Orléans (Marie Louise Adélaïde; 13 August 1698 – 10 February 1743) was the third daughter of Philippe d'Orléans, and Françoise Marie de Bourbon, a legitimised daughter of Louis XIV of France and his mistress, Madame de Montespan.
 She was Abbess of Chelles.
Louise Élisabeth de Bourbon-Condé (Louise Élisabeth; 22 November 1693–27 May 1775) was a daughter of Louis III de Bourbon, Prince of Condé, and his wife, Louise Françoise de Bourbon, "légitimée de France", a legitimised daughter of Louis XIV of France and Madame de Montespan.
The Duchy or Duke of Rambouillet was a French Peerage created in 1711 for Louis Alexandre de Bourbon, "Légitimé de France", Count of Toulouse, youngest legitimised son of Louis XIV and Madame de Montespan.
Marie Anne de Bourbon (1666–1739) legitimised daughter of Louis XIV of France and Louise de La Vallière, wife of Louis Armand I, Prince of Conti.

Question: Louise Diane d'Orleans is the youngest legitimised daughter of a monarch of the House of Bourbon who reigned as king of france beginning in what year?
Answer: 1643