HCF and LCM Questions for the CAT are part of the Quantitative Aptitude section in the CAT exam. LCM means the Least Common Multiple and HCF means the Highest Common Factor. The difficulty level of the HCF and LCM questions can be easy to moderate.
What are some important formulae for HCF & LCM for CAT?
- Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.
- Suppose we have to find the H.C.F. of two given numbers. Divide the larger number by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the required H.C.F.
- Suppose we have to find the H.C.F. of three numbers. Then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given numbers. Similarly, the H.C.F. of more than three numbers may be obtained.
- Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.
- Arrange the given numbers in a row in any order. Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
HCF & LCM Tricks for the CAT Exam
- If the difference between two numbers is a factor of both, then their HCF is that Factor
- For fractions, HCF = HCF of numerators / LCM of denominators
- If HCF and LCM of two numbers are known, the numbers can be found using the formula: HCF * LCM = Product of the numebers
HCF & LCM Concepts for the CAT Exam
In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers without decimal point, find
H.C.F. or L.C.M. as the case may be. Now, in the result, mark off as many decimal places as are there in each of the given numbers.
Find the L.C.M. of the denominators of the given fractions. Convert each of the fractions into an equivalent fraction with L.C.M. as the denominator, by multiplying both the numerator and denominator by the same number. The resultant fraction with the greatest numerator is the greatest.
What are some CAT-level HCF & LCM Practice Questions?
Q 1. The greatest number which on dividing 1665 and 2037 leaves reminders 6 and 5 respectively is,
A. 123
B. 127
C. 235
D. 305
Answer: B
Q 2. Which of the following has the most number of divisors?
A. 99
B. 101
C. 176
D. 182
Answer: C
Q 3. The HCF of 9/10, 12/25, 18/35 and 21/40 is:9
Answer: 3/1400
Q 4. If the sum of two numbers is 55 and the HCF and LCM. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the number is equal to:
A. 55/601
B. 601/55
C. 11/120
D. 120/11
Answer: C
Q 5. The LCM of two numbers are 48. The numbers are in the ratio 2: 3. Then sum of the number is:
A. 28
B. 32
C. 40
D. 64
Answer: C
Q 6. Find the highest common factor of 72, 90, and 126
A. 24
B. 18
C. 20
D. 52
Answer: B
What are the must-do HCF & LCM questions for the CAT exam?
Q 7. Find the LCM of 12, 15, 18
A. 140
B. 160
C. 170
D. 180
Answer: D
Q 8. Find the HCF of 60 and 114
A. 6
B. 8
C. 10
D. 12
Answer: A
Q 9. Find the LCM of 24 and 90.
A. 180
B. 360
C. 420
D. 560
Answer: B
Q 10. Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case.
A. 140
B. 142
C. 144
D. 146
Answer: C
Q 11. Two tankers contain 850 litres and 680 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both tankers when used an exact number of times.
A. 170
B. 180
C. 190
D. 200
Answer: A
What were the previous year's CAT HCF & LCM questions?
Q 12. Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case.
A. 7
B. 36
C. 144
D. 151
Answer: D
Q 13. Find the LCM of 40, 48 and 45
A. 720
B. 733
C. 777
D. 789
Answer: A
Q 14 Find the LCM of 20, 25 and 30.
A. 100
B. 200
C. 300
D. 400
Answer: C
Q 15 Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder of 7 in each case.
A. 12
B. 16
C. 133
D. 144
Answer: D
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