Question

the HCF and LCM of two numbers are 33 and 264 respectively.when the first number is completely divided by 2 the quotient is 33 the other number is
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Answer 1

Answer:

132

Step-by-step explanation:

HCF X LCM = 1st number X 2nd number

HCF = 33

LCM = 264

FIRST NUMBER = 2*33=66

SECOND NUMBER = x

33*264 = 66*x

66x = 33*264

x = 33*264 / 22

x= 132

Answer 2

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✰Answer✰

♦️GiveN

• HCF of two numbers = 33
• LCM of two numbers = 264
• One number is divisible by 2, and when divided, Quotient = 33

♦️To FinD

• Other number....?

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✰Concept to be used✰

➯Euclid' s Division lemma

For any two positive integers a and b ,there exists q and r such that a = bq+r

➯In simple words,

$\boxed{\rm{ \red{dividend = divisor \times quotient + remainder}}}$

➯Relation of HCF, LCM and product of numbers

The product of two numbers is also the product of its LCM and HCF

➯In simple words,

$\boxed{ \rm{ \red{HCF \times LCM = product \: of \: numbers}}}$

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✰Solution✰

➯One of the number is divisible by 2, So remainder is 0 . When the number is divided by 2, Quotient = 33

➯So by using EDL,

$\rm{ \rightarrow \: dividend = 2 \times 33 + 0} \\ \\ \rm{ \rightarrow \: dividend = 66} \\ \\ \therefore{ \rm{ \boxed{ \purple{ \rm{first \: number \: is \: 66}}}}}$

➯We have, our HCF = 33 and LCM= 264

One of the number = 66

➯By Using relation ,

$\rm{ \rightarrow \: 33 \times 264 = 66 \times 2nd \: number} \\ \\ \rm{ \rightarrow \: 2nd \: number = \frac{ \cancel{33 }\times 264}{ \cancel{66} \: 2} \: } \\ \\ \therefore \boxed{ \purple{ \rm{\: 2nd \: number = 132}}}$

♦️Thus, Our required answer is 132.

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