The LCM of two numbers is 4 times HCF. If the sum of LCM and HCF is 45, and one of the numbers is 9, then find the sum of the squares of those numbers.
Answers
Answer:
1377
Step-by-step explanation:
One number=9
Let other number=a
LCM(9,a)=4×HCF. (1)
According to question:-
LCM+HCF=45. (2)
from (1)
4 HCF+HCF=45
5HCF=45
HCF=45/5
HCF=9
hence, HCF(9,a)=9
putting this value in (2)
LCM+9=45
LCM=45-9
LCM=36
We know that product of LCM and HCF of two numbers is equal to product of the two numbers,
that is,
PRODUCT OF LCM AND HCF OF 2 NUMBERS=PRODUCT OF TWO NUMBERS
Therefore,
LCM×HCF=9×a
36×9=9×a
324=9a
324/9=a
36=a
hence, other number is 36.
NOW, sum of squares of numbers:
= 9^2+36^2
= 81+1296
= 1377
Given:
LCM = 4*HCF
LCM + HCF= 45
One of the numbers= 9
To find:
Sum of squares of the two numbers
Solution:
LCM = 4*HCF
Substituting the value of LCM in the equation- LCM + HCF= 45
So, 4HCF + HCF = 45
So, 5HCF = 45
Or, HCF= 9
So, the LCM = 36
As we know, LCM * HCF= Number 1* Number 2
Number 1 is given as 9
So, placing all the values, we get- Number 2 = (36*9)/9 = 36
The two numbers are 9 and 36
So, the squares of two numbers are = 36^2 + 9^2 = 1296+81 = 1377