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You can make a list of possible pairs of numbers that have a LCM of $48$ ?

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True

False

answer is A.

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Detailed Solution

First, we will find Factors of 48.

48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

So, the list of pair of numbers which have LCM equal to

48

are,

(1, 48), (2, 48), (3, 48), (4, 48), (6, 48), (8, 48), (! 2, 48), (16, 48), (24, 28), (48, 48)

We can also see divisor

3

and

16

are co-prime numbers.
Co-prime number’s LCM is equal to their product.
Now, we add multiples of

3

and

16

in list of factor of

48

that have their LCM equal to

48

(3, 16), (6, 16), (12, 16), (24, 16)

Here, the list of numbers whose LCM equal to

48

are -

(3, 16), (6, 16), (12, 16), (24, 16), (1, 48), (2, 48), (3, 48), (4, 48), (6, 48), (8, 48), (12, 48), (16, 48),

(24, 48), (48, 48)

.
∴ Hence, option 1, true is correct answer that is it has a list of possible pairs of numbers that have a LCM of

48

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