Answer to Question #121341 in Combinatorics | Number Theory for Promise

Question

The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….

Answer 1

There is no solution, because:

1. 64 is not divisible by 11.

2. 368 is not divisible by 11.

3. 368 is not divisible by 64.

Example

The HCF of two numbers is 11, and their L.C.M is 330. If one number is 66, then the other number is …

Let the first number be $11a=66=>a=6,$ the second number be $11b.$ Then

$11ab=330 c,$ $a$ and $b$ are relatively prime.

Hence

$$6b=30c=>b=5, c=1$$

The HCF of two numbers is 11, and their L.C.M is 330. If one number is 66, then the other number is 55.