H.C.F. and L.C.M.

1. Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?
A. 28	B. 40
C. 64	D. 42

Answer : Option B

Explanation :

Let the numbers be 2x and 3x

LCM of 2x and 3x = 6x (∵ LCM of 2 and 3 is 6. Hence LCM

of 2x and 3x is 6x)

Given that LCM of 2x and 3x is 48

=> 6x = 48

=> x = ⁴⁸⁄₆ = 8

Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40

2. What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
A. 9800	B. 9600
C. 9400	D. 9200

Answer : Option B

Explanation :

Greatest number of four digits = 9999

LCM of 15, 25, 40 and 75 = 600

9999 ÷ 600 = 16, remainder = 399

Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75

= 9999 - 399 = 9600

3. Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
A. 40	B. 30
C. 20	D. 10

Answer : Option C

Explanation :

Let the numbers be 2x, 3x and 4x

LCM of 2x, 3x and 4x = 12x

=> 12x = 240

=> x = ²⁴⁰⁄₁₂ = 20

H.C.F of 2x, 3x and 4x = x = 20