model 1 Basic formula of LCM & HCF Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Using Rule 1 :

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

LCM = ${Product of two numbers}/ {HCF}$ = $4107/37$ = 111

Obviously, numbers are 111 and 37 which satisfy the given condition.

Hence, the greater number = 111

Answer: (c)

Using Rule 1 :

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

First number × Second number = HCF × LCM

⇒ 75 × Second number = 15 × 225

∴ Second number = ${15 × 225}/75$ = 45

Answer: (a)

HCF = 12

Numbers = 12x and 12y

where x and y are prime to each other.

∴ 12x × 12y = 2160

⇒ xy = $2160/{12 × 12} $

= 15 = 3 × 5, 1 × 15

Possible pairs = (36, 60) and (12, 180)

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

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: (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