Question

The HCF and the LCM of two digits no. Are 2 and 644 respectively. Find the numbers
Answer is 28 and 46
but how??

Answer 1

Let the numbers be 2x and 3x

LCM of 2x and 3x = 6x (∵ LCM of 2 and 3 is 6. Hence LCM

of 2x and 3x is 6x)

Given that LCM of 2x and 3x is 48

=> 6x = 48

=> x = 48⁄6 = 8

Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40

Answer 2

Answer:

The correct answer will be -

28, 46

14, 92

Step-by-step explanation:

Given in the question

HCF of the given two numbers is = 2

LCM of the two numbers is = 644

Now,

Let the numbers be x and y.

If we factorize 644 we will get

644 = $2\times2\times7\times23$

A given the HCF is 2.

The numbers formed will have at least 2 as their factors. Also, only one number will have both 2 as factors because HCF is 2.

Writing such number one combination will be,

x = $2\times2\times 7$ = 28

y = $2\times 23$ = 46

Another combination can be -

x = $2\times 2\times23$ = 92

y = $2\times 7$ = 14

So two possible pairs are (28, 46) and (14, 92)

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