KUALA LUMPUR, Malaysia (AP) _ Nancy Reagan joined students in singing ''Our World Without Drugs'' today at an exhibition against what Malaysia regards as its biggest problem: drug abuse.

Joined by Dr. Siti Hasmah, wife of Prime Minister Mahathir Mohamad, Mrs. Reagan sat in the front row of a class at Selangor Science High School and listened to students discussing the drug menace.

In response to questions by a teacher, the students decided that drug abuse, child abuse, crime and unemployment, in that order, were the main problems facing their society. The class' answers appeared to have been rehearsed in advance.

The school was chosen for its convenient location rather than being a site of drug abuse among scholars. ''We have no drug problem here,'' said Vice Principal Adnan Ibrahim.

The elite boarding school offers full government scholarships to the best and brightest young Malaysians. Hundreds of uniformed students waved U.S. and Malaysian flags as Mrs. Reagan arrived on a hot, overcast day.

The lyrics to ''Our World Without Drugs'' alternated between the English and Malay languages. Mrs. Reagan smiled when the words turned to Malay, threw up her hands and stopped singing.

The class presented her with a button with the words ''Be a Dadah Buster'' and a drawing of a clenched first crushing a syringe.

Dadah is the odious label used for all controlled substances that are abused. When the button was pinned to her blouse, Mrs. Reagan said, ''You are so right on the button.''

Later, Mrs. Reagan departed for a short visit in Bangkok, Thailand, a country where much of the world's opium and other drugs have originated. On Monday, she will rejoin her husband, President Reagan, in Tokyo, where he will be attending the seven-nation economic summit.

Mrs. Reagan's plane was an hour late taking off for Bangkok because of a thunderstorm and poor visibility.

In Kuala Lumpur, Mrs. Reagan listened to personal tales of woe from a former drug addict and the mother, father and two wives of recovering abusers.

Mrs. Rohani Mat, 38, whose addict son has not fully recovered, sobbed, ''What can I do?'' Mrs. Reagan appeared shaken and patted the woman on her shoulder several times while trying to console her.

Mrs. Reagan brought her anti-drug abuse campaign to Malaysia at the invitation of Dr. Siti, who attended a conference of first ladies in Washington in April 1985.

''She's happy with the work we are doing here. As a medical doctor, I was aware of the drug problem but my visit to Washington made me get into these projects more,'' Dr. Siti told reporters.

''It has strengthened my resolution to contribute more to eradicate the problem.''