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

Answer: (b)

HCF of two-prime numbers = 1

∴ Product of numbers = their LCM = 117

117 = 13 × 9 where 13 & 9 are co-prime. L.C.M (13,9) = 117.

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: (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