Two numbers have an H.C.F of 11 and an L.C.M of 7700. If one number is 275, find the other__________?
Show answer Hide answer
Answer: C. 308
Explanation
The product of any two positive integers always equals the product of their HCF and LCM. Multiplying the highest common factor of eleven by the lowest common multiple of seventy seven hundred gives eighty four seven hundred. Dividing this product by the given number of two75 results in the other number, three hundred eight. The highest common factor divides evenly into both numbers without leaving any remainder. The lowest common multiple is the smallest positive integer divisible by both given numbers. Number theory proves that the product identity holds true for any pair of integers.
Cryptographic algorithms utilize number theory principles like LCM and HCF for data security systems. Engineers apply common multiple concepts to synchronize repetitive mechanical gear cycles. Fractions simplification in advanced mathematics relies heavily on finding common factors and multiples. Option A is incorrect because it does not satisfy the required product relationship with the LCM. Option B fails the fundamental divisibility tests associated with the given HCF and LCM values. Option D overestimates the resulting number and fails the product identity check.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the largest five-digit integer that is evenly divisible by 32, 36, 40, 42, and 48_________?
Show answer Hide answer
Answer: D. 90720
The least common multiple of all the given divisor numbers is calculated as fifty zero forty. Dividing the largest five digit number by this least common multiple identifies the scaling multiplier. Multiplying the least...
Q2. Two right circular cones have heights in a 1:2 ratio and base perimeters in a 3:4 ratio. What is the ratio of their volumes_________?
Show answer Hide answer
Answer: C. 9:32
Cone volume is proportional to the square of the base radius multiplied by height. Base perimeters ratio equals the base radii ratio, which is given as 3 to 4. Squaring radii and multiplying by height ratio yields a volu...
Q3. A cuboid has dimensions of 4 cm, 5 cm, and 6 cm. Determine its volume?
Show answer Hide answer
Answer: A. 120 cm3
Volume of a cuboid = length * breadth * height = 4 * 5 * 6 = 120 cm3, but the option unit is incorrectly written as cm2 in option B, whereas A has cm3.
Q4. What is the effective annual interest rate for a nominal rate of 6% per annum payable semi-annually:_______?
Show answer Hide answer
Answer: D. Rs 6.09%
Semi annual compounding divides the nominal annual interest rate by two for each compounding period. The effective annual rate formula squares the semi annual growth factor and subtracts one. Computing this expression re...
Q5. Find the G.C.D of 1.08, 0.36, and 0.9________?
Show answer Hide answer
Answer: C. 0.18
Decimal numbers are converted to integers by multiplying by a common power of ten. Finding the greatest common divisor of 108, 36, and 90 yields 18. Moving the decimal back two places gives the correct GCD of 0.18. Great...
Q6. Two numbers in a 2 : 3 ratio have an L.C.M of 48. What is their sum_________?
Show answer Hide answer
Answer: C. 40
Representing two numbers in a two to three ratio as two x and three x helps find their LCM. The least common multiple of these proportional terms equals six x which is set to forty eight. Solving for x gives eight making...