Question

Two different composite numbers A and B are factorised as:

$A = (5^p \times 2q)$ and $B = (3^p \times 2^q)$, where $p$ and $q$ are WHOLE numbers.

If LCM of A and B always ends with 5 which of the following is the HCF of A and B?

• A. 1
• B. 2
• C. 5
• D. 15

Answer 1

Answer: (A)

1

Answer 2

The LCM of numbers always ending with 5 must be odd.
In the factorizations
$A = 5^p \times 2^q$ and $B = 3^p \times 2^q$,
if $q>0$ then the LCM will include a factor of $2$ making it even.
Hence, to ensure the LCM is odd (ends with 5), we must have $q = 0$.
This gives:
$A = 5^p$ and $B = 3^p$.
Since $5$ and $3$ are distinct primes,
the only common factor is $1$.

Thus, the HCF of $A$ and $B$ is 1.