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

Answer: (d)

Using Rule 1 :

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

LCM × HCF = 1st Number× 2nd Number

⇒225 × 5 = 25 × x

∴ x = ${225 × 5}/25$ = 45

Answer: (d)

Using Rule 1 :

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

First number = 2 × 44 = 88

∴ First number × Second number

= H.C.F. × L.C.M.

⇒ 88 × Second numebr

= 44 × 264

⇒ Second number = ${44 × 264}/88$ = 132

Answer: (c)

Using Rule 1 :

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

First number × Second number = HCF × LCM

⇒ 864 × Second number

= 96 × 1296 ⇒ Second number

${96 × 1296}/864$ = 144

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: (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: (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