Question

Find the counting number A, if GCF(A,6)=2 and LCM(A,6)=42

Answer 1

To find the number A when GCF(A,6) = 2 and LCM(A,6) = 42, we use the formula GCF × LCM = Product of the numbers to get A = (2 × 42) / 6, which simplifies to A = 14.

Step-by-step explanation:

To find the counting number A, given that the Greatest Common Factor (GCF) of A and 6 is 2, and the Least Common Multiple (LCM) of A and 6 is 42, we need to use the relationship between GCF, LCM, and the numbers involved which is given by:

GCF(A, B) × LCM(A, B) = A × B

Here, A and B are the numbers for which we are finding the GCF and LCM, 2 and 42 are their GCF and LCM respectively, and 6 is the number B.

Using this formula:

2 × 42 = A × 6

Divide both sides of the equation by 6 to find A:

A = (2 × 42) / 6

A = 84 / 6

A = 14

Therefore, the counting number A is 14.

Answer 2

The value of A is 14.

Step-by-step explanation:

We have LCM of (A,6) = 42

Assume A as 42/6 = 7

But we also have GCF (A,6) = 2

7 cannot be divided by 2 so, value of A is not 7.

Assuming next value,

A = 42 x 2 / 6 = 14

We know that LCM of 14 and 6 is 42

GCF of 14 and 6 is 2.

The value of A is 14.