model 5 lcm & hcf vs ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Using Rule 1,

1st number × 2nd number = L.C.M. × H.C.F

Let the numbers be 3x and 4x respectively

First number × second number

= HCF × LCM

⇒ 3x × 4x = 2028

⇒ $x^2 = 2028/{3×4}$ = 169

∴ x = $√{169}$ = 13

∴ Sum of the numbers

= 3x + 4x = 7x = 7 × 13 = 91

Answer: (a)

Let the two numbers are 2x and 3x respectively.

According to question,

LCM = 54

x (3×2)= 54

⇒ x = 9

Numbers = 2x = 2 × 9 = 18

and, 3x = 3 × 9 = 27

Sum of the two numbers

= 18 + 27 = 45

Answer: (a)

Let the numbers be 4x and 4y

where x and y are prime to each other.

LCM = 4xy

∴ $(\text"4x+4y")/ \text"4xy"$ = $7/12$

⇒ 12 (x + y) = 7 xy

⇒ x = 3, y = 4

∴ Smaller number = 4 × 3 = 12

Answer: (a)

If the numbers be 2x and 3x,

then LCM = 6x

∴ 6x = 48 ⇒ x = 8

∴ Required sum = 2x + 3x = 5x

= 5 × 8 = 40

Answer: (a)

Let the number be 3x and 4x.

Their LCM = 12x

According to the question,

12x = 240

⇒ x = $240/12$ = 20

∴ Smaller number = 3x = 3 × 20 = 60

Answer: (d)

Using Rule 1,

1st number × 2nd number = L.C.M. × H.C.F

Product of two numbers

= HCF × LCM

⇒ Numbers = zx and zy

∴ zx × zy = z × LCM

⇒ LCM = xyz