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

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: (b)

Numbers = 3x and 4x

HCF = x = 4

∴ LCM = 12x = 12 × 4 = 48

Answer: (b)

L.C.M. of 28 and 42

= 2 × 2 × 7 × 3 = 84

H.C. F. of 28 and 42

∴ H.C. F = 14

Required ratio = $84/14$ = 6 : 1

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 numbers be 3x and 4x.

∴ Their LCM = 12x

∴ 12x = 84

⇒ x = $84/12$ = 7

∴ Larger number = 4x = 4 × 7 = 28

Answer: (a)

If the numbers be 2x and 3x,

then LCM = 6x

∴ 6x = 48 ⇒ x = 8

∴ Required sum = 2x + 3x = 5x

= 5 × 8 = 40