Q1.
Find the HCF of 144, 180, and 192 .
Solution.
HCF = 12 .
Solution
Q2.
HCF and LCM of two number are 21 & 84. the ratio of two numbers are 1;4 . Find the smallest number.
21 x 84 = 4x2
x : 4x (given)
x = 21
or
Direct multiply HCF by ratio
21 x 1 = 21
So, lowest number is 21 .
Solution
Q3.
Find the HCF of xyz and mnp.
Solution.
1
Note : there is no common factor .
Solution
Q4.
The sum of two numbers is 84, whose HCF is 12 . Find the total pairs of such numbers.
Solution.
The ratio of two numbers is x:y
So, 12x + 12y = 84
x + y = 7
pairs are (1,6),(2,5),(3,4)
Total pairs are three .
Solution
Q5.
The product of two numbers are 4107 , its HCF is 37 . Find the largest number .
Solution.
Let the numbers are in ratio x:y
So number are 37x and 37y
37x . 37y = 4107
xy = 3
In this case x = 1 , y = 3
So, largest value is 37y = 37 x 3 = 111
smallest value is 37x = 37 x 1 =
37
Answer = 111
Solution
Q6.
Two numbers are in ratio 3:4 and their LCM is 48. Find the difference of these two numbers.
Solution.
Let numbers are 3x and 4x , their HCF is x
first number x second number = HCF x LCM
(3x) x (4x) =
(x) x 48
x = 4
So numbers are 3x = 3 x 4 = 12 and 4x = 4 x 4 = 16
difference of the
two numbers = 16 - 12 = 4
Solution
Q7.
Two numbers are in ratio of 4:5 , and LCM is 180 , find both the numbers .
Solution.
(4x) x (5x) = (x) x 180
x = 9
Numbers are 4x = 36 and 5x = 45
Note : Let numbers are 4x and 5x , their LCM is 180 and HCF is x .
find number x second number =
HCF x LCM
Solution
Q8.
Find the least square number that can be divisible by 36, 40 and 48 .
Solution.
LCM of 36, 40 and 48 = 24 x 32 x 5
Required number = 24 x 32
x 52 = 3600
Solution
Q9.
Sum of two numbers is 40 and difference is 1/5 of the sum . find LCM and HCF .
Solution.
Let numbers are x and y
x + y = 40
x - y = 8
x = 24, y = 16
LCM = 48
HCF = 8
Solution
Q10.
The LCM of three numbers are 120, which number cannot be HCF of these numbers .
(a) 38 , (b) 8 , (c) 12 , (d) 24
Solution.
38
Note : LCM is divisible by HCF (exactly).
Solution
