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

Whenever a Q talks of product, LCM and HCF of two numbers ............. most likely it will deal with the formula..
Product = LCM * HCF

the two statements give LCM and HCF separately ..
so COMBINED we can get the product as 48*4
suff
C
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Target question: What is the value of the product ab?

Statement 1: The least common multiple of a and b is 48
Let's TEST some numbers.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 48. In this case, ab = (1)(48) = 48
Case b: a = 2 and b = 48. In this case, ab = (2)(48) = 96
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The greatest common factor (aka divisor) of a and b is 4
Let's TEST some numbers (again).
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 8 and b = 4. In this case, ab = (8)(4) = 32
Case b: a = 4 and b = 4. In this case, ab = (4)(4) = 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

When we apply the above rule, we get: (4)(48) = ab
So, ab = 192
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

(GCF)(LCM)=Product
So
From statemnt 1 we get LCM and from statement 2 we get GCF.
So ab=48*4

Hence Answer is C

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

Option C

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?

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.

Answer: C
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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

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?