Lord Advocate Frank Mulholland, prosecuting, was addressing jurors in the trial of Angus Sinclair, who denies raping and murdering Christine Eadie and her friend Helen Scott.
Mr Mulholland told the jury that the girls had suffered a “terrifying” death in “horrific” circumstances.
The 17-year-olds were last seen at Edinburgh’s World’s End pub on October 15 1977.
Christine’s body was found the following afternoon at Gosford Bay, Aberlady in East Lothian, while Helen’s body was discovered a few hours later in a wheat field near Haddington.
Sinclair, 69, is accused of carrying out the attacks with his brother-in-law Gordon Hamilton, who died in 1996.
In his closing speech to the jury who have been hearing five weeks of evidence at the High Court in Livingston, Mr Mulholland said parts of the accused’s story were “ludicrous”.
Sinclair gave evidence earlier this week in which he said he and Hamilton met the girls in the pub and later drove to Holyrood Park in his caravanette, where both men had consensual sex with each girl before they all travelled to East Lothian because he wanted to go fishing.
Sinclair said Hamilton left in the caravanette and he thought the girls were being driven home. He has said they were “alive and unharmed” when he left them.
He told jurors that he only found out what happened to the teenagers after reading about it in a newspaper on the Tuesday.
Mr Mulholland told the jury: “My only regret in this case is that Hamilton is not sitting alongside Sinclair in the dock.”
He said that the suggestion that Hamilton could “overpower” both girls on his own was “ludicrous”.
He said Sinclair’s evidence that Hamilton returned to East Lothian and was “neither up nor down” and that he was “meandering” and not in a hurry to leave the area “does not stack up” and was “devoid of all credibility”.
“In my submission, there’s more chance of Livingston Football Club winning the Champions League than this being true,” Mr Mulholland said.
Mr Mulholland suggested to the jury that the “totality of the evidence is considerable, powerful and quite frankly overwhelming.”
“It exposes as a lie the incredible story put forward by Sinclair on what he says happened that night.”
He added: “I invite you as a jury to return a verdict of guilty to both charges that Angus Sinclair was responsible with his brother-in-law Gordon Hamilton for these appalling murders.”