MCQ
Numerical: LCM and HCF MCQ - Practice Questions with Answers
Solve 15 Numerical: LCM and HCF questions for RAS/RPSC preparation.
Practice questions
Q1The HCF and LCM of two numbers are 12 and 240 respectively. If one number is 48, which statement is correct?
For any two positive integers, HCF × LCM = product of the two numbers. This is the standard relation used when one number is missing. Here, HCF = 12 and LCM = 240, so product of the two numbers = 12 × 240 = 2880. One number is 48. Therefore, the other number = 2880 ÷ 48. Since 48 × 60 = 2880, the other number is 60. Hence the correct statement is that the other number is 60.
Q2Find the highest common factor of 84, 126 and 210.
Use prime factorisation to find the HCF. Here, 84 = 2² × 3 × 7, 126 = 2 × 3² × 7 and 210 = 2 × 3 × 5 × 7. For the HCF, take only the common prime factors with the smallest powers. The common factors are 2, 3 and 7. Therefore, HCF = 2 × 3 × 7 = 42. Hence, the highest common factor of 84, 126 and 210 is 42.
Q3For the numbers 18 and 24, consider these statements: 1. Their HCF is 6. 2. Their LCM is 72. 3. Product of HCF and LCM is 432. Which of the statements are correct?
Prime factorise the two numbers: 18 = 2 × 3² and 24 = 2³ × 3. The HCF uses the smaller powers, so HCF = 2 × 3 = 6. The LCM uses the larger powers, so LCM = 2³ × 3² = 8 × 9 = 72. Now HCF × LCM = 6 × 72 = 432, which is also equal to 18 × 24. Therefore, all three statements are correct.
Q4Three bells ring at intervals of 12 minutes, 15 minutes and 20 minutes. They ring together at 8:00. Which statement is incorrect?
The bells will ring together again after the LCM of their time intervals. Factorise the intervals: 12 = 2² × 3, 15 = 3 × 5 and 20 = 2² × 5. The LCM takes the highest powers of all prime factors, so LCM = 2² × 3 × 5 = 60 minutes. Starting from 8:00, adding 60 minutes gives 9:00. Therefore, the statement saying 8:45 is incorrect.
Q5A number leaves a remainder of 5 when divided by 12, 18 and 30. Which of the following statements about the least such number is incorrect?
If a number leaves the same remainder 5 on division by 12, 18 and 30, then subtracting 5 from it must give a common multiple of 12, 18 and 30. First find the LCM: 12 = 2² × 3, 18 = 2 × 3², and 30 = 2 × 3 × 5. So LCM = 2² × 3² × 5 = 180. The least required number is 180 + 5 = 185. Therefore the statement saying that the least such number is 175 is incorrect.
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More questions
6Find the greatest number that divides 84, 126 and 210 exactly.
7The HCF of two numbers 84 and 126 is 42. What is their LCM?
8Match each pair of numbers with its HCF. P. 18 and 24; Q. 35 and 49; R. 64 and 80. Which matching is correct?
9For the numbers 16, 24 and 36, which of the following statements is incorrect?
10For the numbers 56 and 98, consider the following statements: I. Their HCF is 14. II. Their LCM is 392. III. The product of the two numbers is equal to HCF + LCM. Which statement(s) is/are correct?
11Match each pair of numbers with its HCF: 1. (8, 12), 2. (9, 15), 3. (10, 25). Which matching is correct?
12Match each pair with its HCF: pair 1: 18 and 30, pair 2: 24 and 40, pair 3: 35 and 56.
13Three bells ring at intervals of 12 seconds, 18 seconds and 30 seconds. If they ring together at 10:00:00, after how much time will they ring together again?
14The HCF and LCM of two numbers are 12 and 180 respectively. If one number is 36, find the other number.
15Three bells ring at intervals of 12 minutes, 15 minutes and 20 minutes. If they ring together at 9:00 a.m., after how many minutes will they ring together again?