HCF and LCM
9 solved SSC CGL Quantitative Aptitude previous year questions on HCF and LCM, each with the correct answer and a full explanation.
Q1
In finding the HCF of two numbers by division method, the last divisor is 17 and the quotients are 1,11 and 2 , respectively. What is sum of the two numbers?
✓ Correct answer: b) 816
ExplanationAs we know, Divided = Divisor × quotient + remainder Divided = 17 × 2 + 0 Divided = 34 Again, Divided = Divisor × quotient + remainder Divided = 34 × 11 + 17 Divided = 374 + 17 = 391 Again, Divided = Divisor × quotient + remainder Divided = 391 × 1 + 34 Divided = 391 + 34 = 425 The two numbers are 425 and 391 Sum of two numbers = 425 + 391 = 816 Hence, Option B is the correct answer.
Q2
LCM and HCF of two numbers are 90 and 15 , respectively. If the sum of the two numbers is 75 , then find the greater number.
✓ Correct answer: a) 45
ExplanationLet the numbers are 15a and 15b respectively.Also, let the greater number be 15a.15ab = 90 ⇒ ab = 6…..(1) 15a + 15b = 75 ⇒ a + b = 5…..(2) From (1) and (2) we get: a = 3, b = 2 So, the greater number = 15 × 3 = 45 Hence, the correct answer is (A).
Q3
What is the largest common divisor of the numbers 1026, 2268 and 2430?
✓ Correct answer: b) 54
ExplanationAccording to the question 1026 = 2 × 3 × 3 × 3 × 19 2268 = 2 × 2 × 3 × 3 × 3 × 3 × 7 2430 = 2 × 3 × 3 × 3 × 3 × 3 × 5 Largest common divisor = 2 × 3 × 3 × 3 = 54 Hence, the correct answer is (B).
Q4
What is the smallest perfect square which is completely divisible by each of 16,18 and 36 ?
✓ Correct answer: a) 144
ExplanationGven numbers are = 16 , 18 and 36 LCM of numbers = 144 is also a perfect square Hence, Option A is the correct answer.
Q5
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
✓ Correct answer: b) 168
ExplanationLCM of 3, 4, 6, 7, 8, 12 = 168 seconds After 168 seconds, they will toll together again.Hence, Option B is the correct answer.
Q6
The ratio of two numbers is 5 : 4 and their HCF is4. What is their LCM?
✓ Correct answer: a) 80
ExplanationRatio of numbers = 5:4 Let the numbers be 5k and 4k.Then, k = 4 (because HCF = 4) Numbers are 20 and16. LCM of 20 and 16 =80. Hence, option A is the correct answer.
Q7
Choose the correct statement from the following.
✓ Correct answer: b) HCF of two or more numbers is the highest number which perfectly divides all the given numbers.
ExplanationAccording to the given options: HCF of two or more numbers is the highest number which perfectly divides all the given numbers.Hence, the correct answer is (B).
Q8
The largest three-digit number that gives the same remainder 2 when divided by 3, 5 and 9 is ________.
✓ Correct answer: d) 992
ExplanationTo find the largest three-digit number that gives the same remainder of 2 when divided by 3, 5, and 9, we first need to find the least common multiple (LCM) of these three divisors.LCM(3, 5, 9) =45 Now we need to find the largest three-digit multiple of 45 and add the remainder (2) to it.The largest three-digit multiple of 45 is 990 ( ) Now, add the remainder 2 to this multiple: 990+2=992 So, the largest three-digit number that gives the same remainder 2 when divided by 3, 5, and 9 is =992 Hence, Option D is the correct answer.
Q9
Find the least number divisible by and 18 , which is a perfect square.
✓ Correct answer: a) 900
ExplanationL.C.M of 2 , 3, 5 ,6, 9 and 18 = 90 and, least number multiple of 90 which is a perfect square is 900. Hence, Option A is correct
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