16. 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

17. 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

18. 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

19. What is the lowest common multiple of 12, 36 and 20?

A. 160 B. 220 C. 120 D. 180

**Answer : Option D**

Explanation :

LCM OF 12,36,20= 180

20. What is the least number which when divided by 5, 6, 7 and 8 leaves a

remainder 3, but when divided by 9 leaves no remainder?

A. 1108 B. 1683 C. 2007 D. 336

**Answer : Option B**

Explanation :

LCM of 5, 6, 7 and 8 = 840

Hence the number can be written in the form (840k + 3) which is divisible by 9

If k = 1, number = (840 × 1) + 3 = 843

which is not divisible by 9

If k = 2, number = (840 × 2) + 3 = 1683

which is divisible by 9

Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a

remainder 3, but when divided by 9 leaves no remainder

21. The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is25, then the other is:

A. 30 B. 28 C. 24 D. 20

**Answer : Option A**

Explanation :

Product of two numbers = Product of their HCF and LCM.

Let one number = x

25×x =5×150

x= (5×150)÷25

X=30

22. 504 can be expressed as a product of primes as

A. 2 × 2 × 3 × 3 × 7 × 7

B. 2 × 3 × 3 × 3 × 7 × 7

C. 2 × 3 × 3 × 3 × 3 × 7

D. 2 × 2 × 2 × 3 × 3 × 7

**Answer : Option D**

Explanation :

It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7

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