The GCD and LCM of two numbers a & b are respectively, 27 and 2079. If a is divided by 9 then the quotient is 21. Then b is:

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243

189

113

297

answer is D.

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Detailed Solution

Given,
Two number = a and b

a

is divided by 9 then quotient = 21
Two number of Greatest common divisor GCD gives = 27
Two number of lowest common multiple LCM gives = 2079
Now, we know that,
GCD

\times

LCM=product of the numbers
The product of two number

a \times b

27 \times 2079 = a \times b

…………..(1)
As per given question
When

a

is divided by 9 then quotient = 21

dividend = divisor \times quotient + remainder

a = 9 \times 21 + 0

\Rightarrow a = 9 \times 21

Put the value ‘a’ in equation (1),

27 \times 2079 = a \times b

27 \times 2079 = 9 \times 21 \times b

\Rightarrow \frac{27 \times 2079}{9 \times 21} = b

b = 297

Hence the value of b = 297.
Correct option is 4.

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