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# If a and b are positive integers, what is the value of the product ab?

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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
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(GCF)(LCM)=Product
So
From statemnt 1 we get LCM and from statement 2 we get GCF.
So ab=48*4

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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
carcass
If a and b are positive integers, what is the value of the product ab ?

(1) The least common multiple of a and b is 48.

(2) The greatest common factor of a and b is 4.

LCM(a,b) * HCF(a*b) = a*b

Option C
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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
re:

Case b: a = 2 and b = 48. In this case, ab = (2)(48) = 96

Isnt' the least common multiple of 2 and 48 -> 48?
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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
carcass
If a and b are positive integers, what is the value of the product ab ?

(1) The least common multiple of a and b is 48.

(2) The greatest common factor of a and b is 4.
Solution:

We need to determine the value of the product ab, given that a and b are positive integers.

Statement One Alone:

Knowing that the least common multiple (LCM) of a and b is 48 is not sufficient. For example, if a = 1 and b = 48, then ab = 48. However, if a = 2 and b = 48, then ab = 96.

Statement Two Alone:

Knowing that the greatest common factor (GCF) of a and b is 4 is not sufficient. For example, if a = 4 and b = 8, then ab = 32. However, if a = 4 and b = 12, then ab = 48.

Statements One and Two Together:

Knowing both values of the LCM and GCF of a and is sufficient since we have a formula that relates the two:

LCM(a, b) * GCF(a, b) = a * b

Therefore, ab = 48 * 4 = 192.

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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
LLM1500
re:

Case b: a = 2 and b = 48. In this case, ab = (2)(48) = 96

Isnt' the least common multiple of 2 and 48 -> 48?
Yes - but you want AB to be the same

a=1 b = 48 --> LCM = 48 and ab= 48

if your replace a=1 with a=2 then ab becomes 96
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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
Is the rule valid for any quantity of numbers?
In other words, will (HCF of a,b,c, ...n) X (LCM of a,b,c, ...n) = a X b X c X ....n?
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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
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Re: If a and b are positive integers, what is the value of the product ab? [#permalink]
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