Question

the difference of lcm and hcf of two numbers is 1572 and the sum of their lcm and hcf is 1596 if the one of the number is 144 and the other is

Answer 1

solution:-
given,one of the numbers=144
let the other no.=a
let, L.C.M of 144 and be 'x'
and let the H.C.F of 144 and a be 'x'
=> x+y =1596.....(¡)
and, => x-y =1572.....(¡¡)
adding both the eq.(¡) and (¡¡)
x+y=1596
x-y 1572
=>2x =3186
now, 2x=3186
=>x=3168/2
=>x=1584.
putting the value of x=1584 in eq.(¡)
we get,
x+y=1596
=>1584+y =1596
=>y= 1596-1584
=>y=12
so, LCM of 144 and a=1584.
and, HCF of 144 and a=12.
we know that,
LCM × HCF = product of the no.
=>1584×12=144×a
=> 144×a=1584×12
=>144a=19008
=>a=19008/144
=>a=132.
so, the other no. is 132.

Answer 2

Given :

• HCF = 1596
• LCM = 1572
• One number = 144

Formula :

$\bf\purple{\fbox{Product\:of\:the\: numbers=HCF×LCM}}$

Assume :

Other number= x

Solution :

Product of the numbers = HCF×LCM

=> 144 × x = 1596×1572

=> x = 1596×1572/144

=> x = 17,423

Answer :

• 17,423 is the other number.

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