Question

Answer plz!
Aman Sir ​

Answer 1

EXPLANATION.

L.C.M and H.C.F.

(b) 200 and 500.

⇒ 200 = 2 x 2 x 2 x 5 x 5. = (2)³ x (5)².

⇒ 500 = 2 x 2 x 5 x 5 x 5. = (2)² x (5)³.

L.C.M = Products of greatest power of each prime factor.

⇒ L.C.M = (2)³ x (5)³.

⇒ L.C.M = 8 x 125.

⇒ L.C.M = 1000.

H.C.F = Product of smallest power of each common prime factor.

⇒ H.C.F = (2)² x (5)².

⇒ H.C.F = 4 x 25.

⇒ H.C.F = 100.

As we know that,

L.C.M x H.C.F = Products of two numbers.

⇒ 1000 x 100 = 200 x 500.

⇒ 100,000 = 100,000.

Hence proved.

(c) 125 and 225.

⇒ 125 = 5 x 5 x 5. = (5)³.

⇒ 225 = 3 x 3 x 5 x 5 = (3)² x (5)².

L.C.M = Products of greatest power of each prime factor.

⇒ L.C.M = (5)³ x (3)².

⇒ L.C.M = 125 x 9.

⇒ L.C.M = 1125.

H.C.F = Product of smallest power of each common prime factor.

⇒ H.C.F = (5)².

⇒ H.C.F = 25.

As we know that,

L.C.M x H.C.F = Products of two numbers.

⇒ 1125 x 25 = 125 x 225.

⇒ 28,125 = 28,125.

Hence proved.

(c) 144 and 136.

⇒ 144 = 2 x 2 x 2 x 2 x 3 x 3. = (2)⁴ x (3)².

⇒ 136 = 2 x 2 x 2 x 17. = (2)³ x (17).

L.C.M = Products of greatest power of each prime factor.

⇒ L.C.M = (2)⁴ x (3)² x 17.

⇒ L.C.M = 16 x 9 x 17.

⇒ L.C.M = 2448.

H.C.F = Product of smallest power of each common prime factor.

⇒ H.C.F = (2)³.

⇒ H.C.F = 8.

As we know that,

L.C.M x H.C.F = Products of two numbers.

⇒ 2448 x 8 = 144 x 136.

⇒ 19,584 = 19,584.

Hence proved.

Answer 2

b) 200 and 500

⇒ 200 = 2 x 2 x 2 x 5 x 5 = 2³ x 5²

⇒ 500 = 2 x 2 x 5 x 5 x 5 = 2² x 5³

L.C.M = 2³ x 5³

= 8 x 125

= 1000

H.C.F = 2² x 5²

= 4 x 25

= 100

LCM x HCF = PRODUCT OF TWO GIVEN NUMBERS

⇒ 1000 x 100 = 200 x 500

⇒ 1,00,000 = 1,00,000

Hence, verified

c) 125 and 225

⇒ 125 = 5 x 5 x 5 = 5³

⇒ 225 = 3 x 3 x 5 x 5 = 3² x 5²

L.C.M = 3² x 5³

= 9 x 125

= 1,125

H.C.F = 5²

= 25

LCM x HCF = PRODUCT OF GIVEN NUMBERS

⇒ 1,125 x 25 = 125 x 225

⇒ 28,125 = 28,125

Hence,verified

d) 144 and 136

⇒ 144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²

⇒ 136 = 2 x 2 x 2 x 17 = 2³ x 17

L.C.M = 2⁴ x 3² x 17

= 16 x 9 x 17

= 2,448

H.C.F = 2³

= 8

LCM x HCF = PRODUCT OF GIVEN NUMBERS

⇒ 2,448 x 8 = 136 x 144

⇒ 19,584 = 19,584

Hence,verified