Question

L C M of the given two number is double the greater number. And the difference between smaller number and HCF is 4 . Therefore the smaller number is

Answer 1

Answer:

by rits

Step-by-step explanation:

(a) 8 is the right answer

Let (x,y)∈N2,x<y(x,y)∈N2,x<y be our ordered pair of two integers.

As x−4x−4 is their greater common divisor,

∃k∈N∗,k(x−4)=y⇒x−4>0⇒x>4(1)(1)∃k∈N∗,k(x−4)=y⇒x−4>0⇒x>4

As their lower common multiple is 2y2y

∃m∈N∗,mx=2y(2)(2)∃m∈N∗,mx=2y

Thus

2k(x−4)=mx⇔(2k−m)x=82k(x−4)=mx⇔(2k−m)x=8

xx has to be a divisor of 88 , so we know that x∈{1,2,4,8}x∈{1,2,4,8}

But, from (1)(1) we know that x∈[5,∞)x∈[5,∞) , so

x∈{1,2,4,8}∩[5,∞)⇔x=8x∈{1,2,4,8}∩[5,∞)⇔x=8