H.C.F and L.C.M of Numbers with Explanation

Q22. Which of the following is a pair of co-primes?

Q23. The product of the L.C.M. and H.C.F. of two numbers is 24. The difference of two numbers is 2. Find the numbers.

Answer- Option A

Explanation-

Let the numbers be x and (x + 2).
Then, x(x + 2) = 24
x² + 2x - 24 = 0
(x - 4) (x + 6) = 0
x = 4.
So, the numbers are 4 and 6.

Q24. The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?

Q25. H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M is 2⁴ x 3⁵ x 5² x 7². The third number is:

Answer- Option B

Explanation-

3240 = 2³ x 3⁴ x 5;
3600 = 2⁴ x 3² x 5²;
H.C.F. = 36 = 2² x 3².
Since H.C.F. is the product of lowest powers of common factors, so the third number must have (2² x 3²) as its factors.
Third number = 2² x 3⁵ x 7².