model 1 Basic formula of LCM & HCF Practice Questions Answers Test with Solutions & More Shortcuts

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)

Using Rule 1 :

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

First number × second number = HCF × LCM

⇒ 84 × second number = 12 × 336

∴ Second number = ${12 × 336}/84$ = 48

Answer: (b)

Using Rule 1 :

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

Second number = ${H.C.F.× L.C.M.}/{First Number}$

= ${27 × 2079}/189$ = 297