Two numbers have an H.C.F of 23, and the remaining factors of their L.C.M are 13 and 14. What is the larger number___________?
Show answer Hide answer
Answer: C. 322
Explanation
Two numbers can be expressed as the highest common factor multiplied by their respective coprime remaining factors. Multiplying the highest common factor twenty-three by each remaining factor thirteen and fourteen gives the two numbers. Comparing the two resulting numbers confirms that the larger number is twenty-three times fourteen, which equals three twenty-two. The least common multiple of two numbers equals their highest common factor multiplied by all coprime factors. Numbers in ratio or factorized form can be reconstructed directly using their highest common factor. Multiplying multi-digit integers requires careful column alignment to ensure calculation accuracy.
Number theory principles are fundamental in cryptography and algorithmic computer science applications. Math competition problems frequently test relationships between highest common factors and least common multiples. Understanding prime factorization helps students solve complex divisibility puzzles efficiently. Option A represents the smaller number formed by multiplying the highest common factor by thirteen. Option B results from an alternate factor combination that does not match the problem parameters. Option D overestimates the product by using an incorrect multiplier with the highest common factor.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. 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...
Q2. 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.
Q3. The ratio of diameters for two spheres is 1:2. What is the ratio of their volumes?
Show answer Hide answer
Answer: C. 1:8
The ratio of the diameters of two spheres is directly proportional to the ratio of their radii, which is one to two. The volume of a sphere is proportional to the cube of its radius according to the standard geometric fo...
Q4. 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...
Q5. 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...
Q6. What is the minimum number of complete years for a sum at 20% compound interest to more than double_________?
Show answer Hide answer
Answer: B. 4
At twenty percent compound interest, the investment growth multiplier each year is one point two. For three years, the multiplier is one point two cubed, equaling one point seven two eight, which is less than doubling. F...