Mathematics carries the highest weight in AISSEE — 150 of 300 marks in Class 6 and 200 of 400 marks in Class 9 — and it is also a key section of the RMS CET. Practise these 10 MCQs on LCM and HCF, then check your answers and step-by-step solutions in the answer key at the end.
Quick facts: AISSEE 2027 will be held on Sunday, 31 January 2027. There is no negative marking, so attempt every question. Online applications are open until 2 December 2026 on exams.nta.nic.in/sainik-school-society.
Practice Questions
Q1. What is the LCM of 15 and 20?
(A) 300
(B) 5
(C) 120
(D) 60
Q2. What is the HCF of 24 and 36?
(A) 6
(B) 24
(C) 12
(D) 72
Q3. Two bells ring at intervals of 8 minutes and 10 minutes. If they ring together now, after how many minutes will they ring together again?
(A) 40 minutes
(B) 80 minutes
(C) 18 minutes
(D) 2 minutes
Q4. The HCF of two numbers is 3 and their LCM is 84. If one number is 12, what is the other number?
(A) 28
(B) 21
(C) 15
(D) 24
Q5. What is the LCM of 18 and 24?
(A) 432
(B) 72
(C) 6
(D) 144
Q6. Two bells ring at intervals of 4 minutes and 10 minutes. If they ring together now, after how many minutes will they ring together again?
(A) 40 minutes
(B) 14 minutes
(C) 20 minutes
(D) 2 minutes
Q7. What is the LCM of 10 and 15?
(A) 150
(B) 5
(C) 60
(D) 30
Q8. What is the HCF of 42 and 56?
(A) 7
(B) 28
(C) 14
(D) 168
Q9. Two bells ring at intervals of 15 minutes and 20 minutes. If they ring together now, after how many minutes will they ring together again?
(A) 60 minutes
(B) 300 minutes
(C) 35 minutes
(D) 5 minutes
Q10. The HCF of two numbers is 4 and their LCM is 60. If one number is 12, what is the other number?
(A) 15
(B) 20
(C) 16
(D) 24
Answer Key with Explanations
(D) 60 — Multiples of 20: the first one divisible by 15 is 60. LCM = 15×20÷HCF(5) = 60.
(C) 12 — The greatest number dividing both 24 and 36 exactly is 12.
(A) 40 minutes — They ring together after LCM(8, 10) = 40 minutes.
(B) 21 — Product of numbers = HCF × LCM, so other = 3×84÷12 = 21.
(B) 72 — Multiples of 24: the first one divisible by 18 is 72. LCM = 18×24÷HCF(6) = 72.
(C) 20 minutes — They ring together after LCM(4, 10) = 20 minutes.
(D) 30 — Multiples of 15: the first one divisible by 10 is 30. LCM = 10×15÷HCF(5) = 30.
(C) 14 — The greatest number dividing both 42 and 56 exactly is 14.
(A) 60 minutes — They ring together after LCM(15, 20) = 60 minutes.
(B) 20 — Product of numbers = HCF × LCM, so other = 4×60÷12 = 20.
How did you score?
9–10 correct: excellent — move on to a full-length mock test. 6–8: good — revise the explanations of the questions you missed. Below 6: study this topic again from your NCERT book and retry these questions after two days.
Free AISSEE / RMS Mock Test
Want a full-length mock test with an All-India rank? Enunciate Academy runs online coaching for Sainik School, RMS, Navodaya and RIMC entrance exams for Class 6 and 9 students across Andhra Pradesh and Telangana. Message us on WhatsApp (94924 44498) to get a free mock test, or see the Spark batch details.
