MCQ: HCF & LCM - 1 - SSC CGL MCQ

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We have,
First number × second number = LCM × HCF

First Number x Second Number = HCF x LCM
Then, 75 x Second Number = 15 x 225
Second Number latex ={ 15 x 225}/75 = 45$
Therefore, other number is 45. 

We know that: 
LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.
Then, LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.
Write the LCM = 120 into factored form, that is
120 = 2 × 2 × 2 × 3 × 5
= 4(2 × 3 × 5)
⇒ 4 is the common factor of the numbers.
So, the HCF of three numbers is a multiple of 4.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Therefore, 35 is not the multiple of 4, then 35 cannot be their HCF.

Product of two numbers = HCF × LCM
1280 = 8 × LCM
160 = LCM

The HCF and LCM of two numbers are 12 and 924.
Let the numbers be 12p and 12q where p and q are prime to each other.
∴ LCM = 12pq
∴ 12pq = 924
⇒ pq = 77
∴ Possible pairs are (1 , 77) and (7 ,11)
Hence , required answer is 2.

HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160

= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Hence , Number of such possible pairs is 2.

Given, LCM = 225, HCF = 5,
First Number = 25 , Second Number = ?
We can find the Second Number with the help of given formula,
"LCM × HCF = 1st Number× 2nd Number"
⇒ 225 × 5 = 25 × 2nd Number

∴ 2nd Number = 45

HCF is 23. So the other two numbers would be,
(23 * 13) and (23 * 14).
Thus Larger Number = 23 * 14 = 322.

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
⇒ 864 × Second number
= 96 × 1296 ⇒ Second number

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We have,
First number × second number = LCM × HCF

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Let LCM be L and HCF be H, then L = 4H
∴ H + 4H = 125
⇒ 5H = 125

∴ L = 4 × 25 = 100

Let the numbers be 23x and 23y where x and y are co-prime.
∴ LCM = 23 xy
As given,
23xy = 23 × 13 × 14
∴ x = 13, y = 14
∴ The larger number = 23y
= 23 × 14 = 322

HCF = 13
Let the numbers be 13x and 13y.
Where x and y are co-prime.
∴ LCM = 13 xy
∴ 13 xy = 455

∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Required number