LCM & HCF — CDS Elementary Mathematics PYQs

If the HCF of $p$ and $q$ $(p>q)$ is $G$, then which of the following statements is/are correct?
I. HCF of $p$ and $(p+q)$ is $G$
II. HCF of $p$, $(p-q)$ is $G$

Select the answer using the code given below:

The HCF and LCM of two numbers $p$ and $q$ are 44 and 4620 respectively. When $p$ is divided by 55, the quotient is 4 and remainder is 0. What is the value of $q$?

What is the LCM of 3.6, 0.009, 0.27?

What is the greatest possible speed at which a person can walk 13.3 km and 20.9 km so that the time (in hours) required in each case is a whole number?

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: LCM of three numbers $p$, $q$ and $r$ $(p>q>r>0)$ is 30 and their HCF is 5. What is the product of the three numbers?
Statement-I: $p=15$
Statement-II: $q=10$

Which one of the following is correct in respect of the above Question and the Statements?

What is the HCF of the polynomials $x^8+x^4+1$ and $x^4+x^2+1$?

Consider the following statements in respect of prime numbers $p$ and $q$:
I. Their LCM is always an odd number.
II. Sum of their LCM and HCF is always an even number.
Which of the statements given above is/are correct?

The HCF of $x$ and $y$ is $H$. Consider the following statements in respect of the HCF of $p=\frac{x^3+y^3}{x^2-xy+y^2}$ and $q=\frac{x^3-y^3}{x^2+xy+y^2}$:
I. The HCF of $p$ and $q$ can be $H$.
II. The HCF of $p$ and $q$ can be $2H$.
Which of the statements given above is/are correct?

What is the HCF of $x^3+y^3+3xy-1$ and $(x+y{)}^4-1$?

What is the LCM of $x^4+x^2{y}^2+y^4$, $x^{3}y+y^4$ and $x^4{y}^2-x^3{y}^3$?