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

Answer: (c)

Answer: (a)

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

Answer: (c)

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

Answer: (c)

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 = ${\text"225 x 5"}/25$

∴ 2nd Number = 45

Answer: (d)

HCF is 23. So the other two numbers would be,

(23 * 13) and (23 * 14).

Thus Larger Number = 23 * 14 = 322.

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.