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

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 numbers be 12x and 12y where x and y are prime to each other.

∴ LCM = 12xy

∴ 12xy = 924

⇒ xy = 77

∴ Possible pairs = (1,77) and (7,11)

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: (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