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

Answer: (c)

HCF of two numbers is 8.

This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60

Answer: (c)

Let the numbers be 6x and 6y where x and y are prime to each other.

∴ 6x × 6y = 216

⇒ xy = $216/{6 × 6}$ = 6

∴ LCM = 6xy = 6 × 6 = 36

Answer: (b)

Using Rule 1 :

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

HCF × LCM = Product of two numbers

⇒ 8 × LCM = 1280

⇒ LCM = $1280/8$ =160

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: (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: (a)

Using Rule 1 :

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

We know that,

First number × Second number = LCM × HCF

⇒ Second number = ${16 × 160}/32$ = 80