Question

LCM of two number P and Q is 2448. HCF of P and Q is a perfect square. Difference between P and Q is same as their HCF. What is the sum of P and Q?

Answer 1

Assume that p > q.

Given :

LCM of p and q = 2448
HCF of p and q = p - q

We know that

LCM × HCF = pq

==> HCF = ( pq) /2448

==> p - q = (pq)/ 2448


2448
= 2× 2× 2 × 2× 3 × 3 × 17

Since p - q is a perfect square,

We can find the product pq such a way that it contains all the factors of 2448 and a perfect square.

p = 153 & q = 144

Now,

p + q = 153 + 144 = 297

I hope this answer helps you

Answer 2

Answer:

Assume that p>q.

Assume that p>q.Given :

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - q

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know that

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 2448

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfect

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfectsquare.

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfectsquare.p = 153 & q = 144

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfectsquare.p = 153 & q = 144Now,

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfectsquare.p = 153 & q = 144Now,p +q = 153 + 144 = 297

Assume that p>q.Given :LCM of p and q = 2448 HCF of p and q =p - qWe know thatLCM x HCF = pa==> HCF = ( pg) /2448==> p - q = (pq)/ 24482448= 2x 2x 2 x 2x 3 x 3 x 17Since p - q is a perfect square,We can find the product pq such a way that it contains all the factors of 2448 and a perfectsquare.p = 153 & q = 144Now,p +q = 153 + 144 = 297I hope this answer helps you