Question

The sum of two numbers is 144 and their lcm is 420 than the smaller number is

Answer 1

➡HERE IS YOUR ANSWER⬇

Let us consider the numbers are Ap and Aq

Now,

lcm (least common multiple)

= Apq

Given that :

Ap + Aq = 144

=> A(p+q) = 144 ...(i)

and

Apq = 420 .....(ii)

Now,

(i)/(ii) =>

(p+q)/pq = 12/35

The only possibility is p = 5 and q = 7.

So, A = 144/12 = 12.

We see that :

p + q = 12 and p - q = 2.

Solving, we get :

p = 7 and q = 5

Therefore, the two numbers are

84 and 60.

So, the smallest number is 60.

⬆HOPE THIS HELPS YOU⬅