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

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: (d)

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

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

Thus Larger Number = 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: (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)

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. 

Answer: (a)

Product of two numbers = HCF × LCM

1280 = 8 × LCM

160 = LCM