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

Answer: (b)

Using Rule 1 :

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

Second number =${HCF × LCM}/{First number} $

= ${18 ×378}/54$ = 126

Answer: (d)

Let the number be 15x and 15y, where x and y are co –prime.

∴ 15x × 15y = 6300

⇒ xy = $6300/{15 ×15}$ = 28

So, two pairs are (7, 4) and (14, 2)

Answer: (c)

LCM = 2 × 2 × 2 × 3 × 5

Hence, HCF = 4, 8, 12 or 24

According to question

35 cannot be H.C.F. of 120.

Answer: (c)

Using Rule 1 :

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

H.C.F. of the two 2-digit numbers = 16

Hence, the numbers can be expressed as 16x and 16y, where x and y are prime to each other.

Now,

First number × second number = H.C.F. × L.C.M.

⇒ 16x × 16y = 16 × 480

⇒ xy = ${16× 480}/{16 ×16}$ = 30

The possible pairs of x and y, satisfying the condition xy = 30 are : (3, 10), (5, 6), (1, 30), (2, 15)

Since the numbers are of 2-digits each.

Hence, admissible pair is (5, 6)

∴ Numbers are : 16 × 5 = 80 and 16 × 6 = 96

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: (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