What is the test for determining whether a defendant had a motive to commit a lewd act?

The trial court instructed the jury with CALCRIM No. 370, which states: "The People are not required to prove that the defendant had a motive to commit any of the crimes charged. In reaching your verdict you may, however, consider whether the defendant had a motive. [] Having a motive may be a factor tending to show that the defendant is guilty. Not having a motive may be a factor tending to show defendant is not guilty." The trial court also instructed the jury on the mental state required for the lewd act chargesi.e., that the People must prove the "defendant committed the act with the intent of arousing, appealing to, or gratifying the lust, passions, or sexual desires of himself or the child." (CALCRIM No. 1110; accord, People v. Martinez, supra, 11 Cal.4th at pp. 442, 452.)