Question

Hello frnds answer these two question pls :-

1.The difference of square of two consecutive numbers is 31. Find the numbers ??

2. Find the the least square number which is divisible by 8, 12 and 16 ??


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Answer 1

1. Let the First Number be : S

As : They are Consecutive Numbers, The Other Number will be : S + 1

Given : The Difference of Square of Two Numbers is 31

⇒ (S + 1)² - S² = 31

⇒ S² + 1 + 2S - S² = 31

⇒ 2S = 30

⇒ S = 15

⇒ The Other Number will be : S + 1 = (15 + 1) = 16

So, The Two Numbers are 15 , 16

2. In order to find the Least Square Number, First we need to Find the LCM of 8, 12 and 16

⇒ The LCM of 8 , 12 , 16 is 48

Now, We need to Prime Factorise , The Number - 48

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 48 = 2² × 2² × 3

In order to make the above expression, Perfect Square - We can notice that We need to Multiply by 3 on both Sides

⇒ 48 × 3 = 2² × 2² × 3²

⇒ 48 × 3 = 144

⇒ The Least Square Number which is Divisible by 8 , 12 , 16 is 144