Question

(i) I am the fifth multiple of the LCM of 2and 7. What number am I ?
(ii) The LCM of the two numbers is 24. Their
sum is 14. What are the numbers ?
(iii) I am the square of the number that is 68 less than the product of the LCM of 2 and 3 and the LCM of 3 and 4. What
number am I?​

Answer 1

(I) I'm 5th multiple of the LCM of 2 and 7. what number am I ?

Answer: 70

L.C.M of 2 and 7 is 14

5th multiple of 14 :

= 14 × 5

= 70

The number is 70.

(ii) Yhe LCM of the two numbers is 24. Their sum is 14. What are the numbers

Answer: 6, 8

Take all the paired values whose sum is 14. And look for the number whose lcm is 24.

• 1 + 13, LCM : 13
• 2 + 12, LCM : 12
• 3 + 11, LCM : 33
• 4 + 10, LCM : 20
• 5 + 9, LCM : 45
• 6 + 8, LCM : 24

6,8 are the numbers whose sum is 14 and their LCM is 24

(iii) I am the square of the number that is 68 less than the product of the LCM of 2 and 3 and the LCM of 3 and 4. What number am I?

Answer: 16

LCM of 2 and 3 = 6

LCM of 3 and 4 = 12

Let the unknown = x

According to the question:

⟹ x = { ( 6 × 12 ) - 68 }²

⟹ x = ( 72 - 68)²

⟹ x = (4)²

⟹ x = 16

The unknown value is 16.