model 1 Basic formula of LCM & HCF 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,

Required number

= ${LCM ×HCF}/{First number}$

= ${864 × 144}/ 288$ = 432

Answer: (b)

Using Rule 1 :

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

First number × second number = HCF × LCM

⇒ 52 × second number = 4 × 520

⇒ Second number =${4 × 520}/52$ = 40

Answer: (a)

Here, HCF = 13

Let the numbers be 13x and 13y where x and y are Prime to each other.

Now, 13x × 13y = 2028

⇒ xy = ${2028}/{13×13}$ = 12

The possible pairs are : (1, 12), (3, 4), (2, 6)

But the 2 and 6 are not co-prime.

∴ The required no. of pairs = 2

Answer: (a)

HCF = 13

Let the numbers be 13x and 13y.

Where x and y are co-prime.

∴ LCM = 13 xy

∴ 13 xy = 455

∴ xy = $455/13$ = 35 = 5 × 7

∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91

Answer: (a)

Using Rule 1 :

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

First number × Second number = HCF × LCM

∴ Second number = ${15 × 300}/60$ = 75

Answer: (c)

Let the numbers be 23x and 23y where x and y are co-prime.

∴ LCM = 23 xy

As given,

23xy = 23 × 13 × 14

∴ x = 13, y = 14

∴ The larger number = 23y

= 23 × 14 = 322