model 1 Basic formula of LCM & HCF Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

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.

Answer: (d)

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.

Answer: (b)

HCF = 12

Numbers = 12x and 12y

where x and y are prime to each other.

∴ 12x × 12y = 2160

⇒ xy = $2160/{12 × 12} $

= 15 = 3 × 5, 1 × 15

Possible pairs = (36, 60) and (12, 180)

Hence , Number of such possible pairs is 2.

Answer: (a)

Product of two numbers = HCF × LCM

1280 = 8 × LCM

160 = LCM

Answer: (b)

Using Rule 1 :

1st number × 2nd number = L.C. M. × H.C.F,

We have,

First number × second number = LCM × HCF

∴ Second number = ${1920 × 16}/128$ = 240