Bissoy.com
Doctors Medicines MCQs Q&A

Two positive numbers A and B are equidistant from 56 and HCF and LCM of A and B is 16 and 192 respectively, then what can be the difference between LCM and HCF of A and 56?

Two positive numbers A and B are equidistant from 56 and HCF and LCM of A and B is 16 and 192 respectively, then what can be the difference between LCM and HCF of A and 56? Correct Answer 440

Given:

HCF = 16

LCM = 192

Formula Used:

First number × Second number = HCF × LCM

Calculation:

Let A and B be at ‘x’ distance from 56.

⇒ A = (56 + x) or (56 – x)

⇒ B = (56 – x) or (56 + x)

Now,

 (56 + x) × (56 – x) = 16 × 192

⇒ 3136 – x2 = 3072

⇒ x2 = 64

⇒ x = 8

A = 64 or 48

⇒ LCM of A and 56 when A is 64 = 448

⇒ HCF of A and 56 when A is 64 = 8

Required difference = 440

⇒ LCM of A and 56 when A is 48 = 336

⇒ HCF of A and 56 when A is 48 = 8

Required difference = 336 – 8 = 328

∴ The required difference is either 440 or 328. 

Related Questions

Consider the following in respect of natural numbers a, b and c: 1. LCM(ab, ac) = a × LCM(b, c) 2. HCF(ab, ac) = a × HCF(b, c) 3. HCF (a, b) < LCM(a, b) 4. HCF(a, b) divides LCM(a, b) Where, a ≠ b ≠ c  Which of the above are correct?
The LCM of two numbers is 28 times their HCF and the sum of their LCM and HCF is 493. The difference of the two numbers is 51. If s is the sum of the two numbers, then what is the sum of digits of s?
Sum of two numbers A and B is 208 (A > B) and HCF of A and B is 16. If A is a perfect square, then what is the ratio of the difference between both the numbers to the difference between LCM and HCF of both the numbers?
There are two numbers A and B (A > B) of two-digits each and their HCF is 18. If LCM and HCF of B and 45 are 270 and 9 respectively and the difference between digits of A is 5, then what is the LCM of A and B?
Consider the following sentences: 1. If a = bc with HCF(b, c) = 1, then HCF(c, bd) = HCF(c, d). 2. If a = bc with HCF(b, c) = 1, then LCM(a, d) = LCM(c, bd). Which of the above statements is/are correct?
Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answer. Quantity A: The LCM of two numbers is 40 times their HCF. The sum of the LCM and HCF is 1,476. If one of the numbers is 288, find the sum of digits of other number? Quantity B: A vendor has 748 oranges, 408 apples and 952 mangoes. If he packs the fruits into crates with an equal number of fruit without mixing them, what is the sum of digits of minimum number of crates required?
The sum of LCM and HCF of two numbers is 536 and the difference between LCM and HCF is. 296. If one of the numbers is 104, then what is the other number ?
Out of three numbers A, B, and C, A is the largest number, and the ratio of B to C is 4 : 5. If HCF of A and B is 16, LCM of B and C is 240, and LCM of A and B is 192, then what is the LCM of A, B, and C?
The LCM of two numbers is 70 times their HCF. The sum of LCM and HCF is 1917. If one of the numbers is 210, then what is the sum of two numbers?
HCF and LCM of two numbers P and Q are 16 and 560 respectively and when 8 is added to P and 20 is added to Q, then HCF and LCM become 20 and 600 respectively, then what is the ratio of the value of P to Q? Assume both P and Q are more than 50.