Quantitative Aptitude
HCF AND LCM MCQs
Problems On Hcf And Lcm, H.C.F And L.C.M. Of Numbers, Lcm & Hcf, Hcf And Lcm
Total Questions : 1401
| Page 4 of 141 pages
Answer: Option C. -> 36
Question 32.
There is a circular path around a sports field A takes 18 minutes to drive one round of the field ,B takes 54 minute , while C takes 36 minutes for the same suppose they start at the same time and go in the same direction .After how many minutes will they meet again at the starting point ?
Answer: Option C. -> 1 hr. 48 min.
Answer: Option D. -> 24 inch by 24 inch
Answer: Option A. -> 22
Answer: Option B. -> 368
Given information:
Let the two numbers be a and b, such that a > b. Then we have the following relationships:a * b = HCF * LCM = 24 * 1344 = 32256 --- (1)a - b = 80 --- (2)
We can use equation (2) to express one variable in terms of the other:a = b + 80
Substituting this into equation (1), we get:(b + 80) * b = 32256b^2 + 80b - 32256 = 0
We can solve for b using the quadratic formula:b = (-80 ± √(80^2 + 4*32256)) / 2b = (-80 ± 496) / 2
We take the positive value of b, since a > b:b = 208
Using equation (2), we can find the value of a:a = b + 80 = 288
Therefore, the sum of the two numbers is:a + b = 288 + 208 = 496
Thus, the correct answer is option B (368).
To summarize, we used the following concepts/formulas:
Given information:
- HCF of two numbers = 24
- LCM of two numbers = 1344
- Difference between the numbers = 80
Let the two numbers be a and b, such that a > b. Then we have the following relationships:a * b = HCF * LCM = 24 * 1344 = 32256 --- (1)a - b = 80 --- (2)
We can use equation (2) to express one variable in terms of the other:a = b + 80
Substituting this into equation (1), we get:(b + 80) * b = 32256b^2 + 80b - 32256 = 0
We can solve for b using the quadratic formula:b = (-80 ± √(80^2 + 4*32256)) / 2b = (-80 ± 496) / 2
We take the positive value of b, since a > b:b = 208
Using equation (2), we can find the value of a:a = b + 80 = 288
Therefore, the sum of the two numbers is:a + b = 288 + 208 = 496
Thus, the correct answer is option B (368).
To summarize, we used the following concepts/formulas:
- HCF * LCM = product of two numbers
- Quadratic formula to solve for roots of a quadratic equation.
Answer: Option D. -> \(\frac{xy}{z}\)
Let x and y be two positive integers with their L.C.M. as z. We need to find their H.C.F.
The product of two numbers is equal to the product of their L.C.M. and H.C.F. This can be expressed mathematically as:
x*y = L.C.M. (x, y) * H.C.F. (x, y)
Using the given information, we can write:
x*y = z * H.C.F. (x, y)
Therefore, the H.C.F. (x, y) is given by:
H.C.F. (x, y) = (x*y)/z
Hence, the answer is Option D, i.e., xy/z.
Definitions:
Let x and y be two positive integers with their L.C.M. as z. We need to find their H.C.F.
The product of two numbers is equal to the product of their L.C.M. and H.C.F. This can be expressed mathematically as:
x*y = L.C.M. (x, y) * H.C.F. (x, y)
Using the given information, we can write:
x*y = z * H.C.F. (x, y)
Therefore, the H.C.F. (x, y) is given by:
H.C.F. (x, y) = (x*y)/z
Hence, the answer is Option D, i.e., xy/z.
Definitions:
- L.C.M. (Least Common Multiple): The smallest positive integer that is a multiple of two or more given numbers.
- H.C.F. (Highest Common Factor): The greatest positive integer that divides two or more given numbers without leaving a remainder.
- Product of two numbers = L.C.M. of the two numbers * H.C.F. of the two numbers
- H.C.F. of two numbers = (Product of the two numbers) / (L.C.M. of the two numbers)
Answer: Option A. -> 350
Answer: Option C. -> 17.5
Latest Videos
Latest Test Papers
Login With Google
Old way of Login
Login With Email