Question

The LCM of two numbers is 15 times thatvof their HCF . if the sum of the LCM and the HCF is 288, find: (i) the HCF and LCM
(ii) the other number, if one number is 54

Answer 1

LCM = 15HCF
LCM + HCF = 288
15HCF + HCF = 288
16HCF = 288
HCF = 18
LCM = 15*18 = 270

Product of numbers = LCM *HCF

x*54= 270*18
x= 90

hope this helps u

Answer 2

i) LET the LCM of the two numbers be y and HCF be x.
So,y=15x
and it is given that the sum of HCF and LCM is 288.
Hence, x+y=288.
Put y=15x in x+y=288.
Therefore, x+15x=288
Hence, x=288/16=18.
Thus,LCM=18*15=270

ii) It is given that one number is 54

Now,
We know that HCF*LCM=Product of the two numbers.

So,18*270=54*a assuming the second number being a.

Thus,4860=54a

This implies that a=4860/54=90

Hence the second number is 90

Hope it helps