Class X Session 2023-24 Question 1

  MATH SAMPLE QUESTION PAPER  

Class X Session 2023-24

   MATHEMATICS STANDARD (Code No.041)

Question 1

If two positive integers a and b are written as  a= x3y2 and b= xy3 , where x, y are prime

numbers, then the result obtained by dividing the product of the positive integers by the

LCM (a, b) is :

(a) xy (b) xy2 (c) x3y3 (d) x2y2


Explanation: 

First, understand the Prime number 

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself

Example of prime Numbers 2, 3 , 5,7,11  , Let's take the number 5 for example. It is only divisible by 1 and itself. Similarly, 11 is also only divisible by 1 and itself.   

Let's understand LCM (Least Common Multiple) of two numbers as an example

Let's find the LCM of 12 and 15. 

To find the LCM, we need to find the smallest multiple that both numbers share

how can you write the Prime factorization of 12: 2×2×3 (A)  


Similarly,   Prime factorization of 15:   3×5 (B)  

Now, we take each prime factor to its highest power from (A)   22

we take each prime factor to its highest power from (B)  31 and 51 both have the same power.

Multiplying these together, we get: LCM(12, 15)

31×51×22 = 60 

Hope above explanation has been cleared now come to the question :

Given  a= x3y2 and b= xy3

LCM(a,b)x3y3

Now, we need to find the result obtained by dividing the product of the positive integers by the LCM(a,b)

The product of the positive integers is  a and b ab= x3y2×xy3 = x4y5 

So, the result obtained by dividing the product of the positive integers by the LCM(a,b)

abLCM(a,b) =x4y5x3y3  

OR

abLCM(a,b) =x4y5x3y3 =x(43)y(53) =x1y2

The correct option is .....?.... comment below 








                                

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