Question

find the LCM and HCF of the following pairs of integers and verify that LCM and HCF = product of the two number 336 and 54 ​

Answer 1

Answer:

Given:- numbers are 336 and 54

$\sf \colorbox{god} {Prime factorisation of 336 and 54 are}$

$⇒336 = (2) ×(168) = (2) × (84)$

$⇒ (2) × (2) × (2) × (42)$

$= (2) × (2) × (2) × (2) × (21)$

$⇒ (2 {)}^{4} \times (3) \times (7)$

$\textbf{and} \: \: 54 = (2) \times (27) = (2) \times (3) \times (9)$

$⇒(2) \times (3) \times (3) \times (3) = (2) \times (3 {)}^{3}$

$\text{HCF \: (336 ,54)}$

$\sf \colorbox{god} {Product of least powers of common factors}$

Verification:

$\sf \colorbox{god} { \: LCM \: (336 ,54) } \times \sf \colorbox{god} {HCF \: 336,54)}$

$⇒6 \times 3024 = (2) \times (3) \times (2 {)}^{4} \times (3 {)}^{3} \times (7)$

$⇒(2 {)}^{4} \times (3) \times (7) \times (2) \times (3 {)}^{ 3} = 336 \times 54$

$\sf \colorbox{god} {= Product of given numbers.}$

$\\ \\ \\ \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙ}$