The Fundamental Theorem of Arithmetic

Find the HCF as well as LCM of $90$ and $144$.

If $p, q$ are two co-prime numbers, then $HCF\left(p, q\right)$ is:

Given that $HCF\left(2520, 6600\right)=120, LCM\left(2520, 6600\right)=252\times k,$ then the value of $k$ is:

Find the largest possible positive integer that will divide $125,162$ and $259$ leaving remainder $5,6$ and $7$ respectively.

$\mathrm{LCM}$ of $\left(2^3\times 3\times 5\right)$ and $\left(2^4\times 5\times 7\right)$ is

Which of the following is a pair of co-primes?

There is a circular path around a sports field. Sonia takes $18$ minutes to drive one round of the field, while Ravi takes $12$ minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Find the $\mathrm{L}\mathrm{C}\mathrm{M}$ and $\mathrm{H}\mathrm{C}\mathrm{F}$ of $336$ and $54$ and verify that $\mathrm{L}\mathrm{C}\mathrm{M}\times \mathrm{H}\mathrm{C}\mathrm{F}=$ product of the two numbers.