State true or false.It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?

A
True
B
False

Solution:

It is required to find whether that HCF and LCM of two numbers can be 24 and 540 are possible.
Fundamental Theorem of Arithmetic states every composite number can be expressed as a product of primes, and this factorization is unique except for the order in which the prime factors occur.
HCF of two numbers

Error parsing MathML: error on line 2 at column 14: Namespace prefix m on semantics is not definederror on line 4 at column 9: Namespace prefix m on mo is not defined

$= 24$ .
LCM of two numbers

Error parsing MathML: error on line 2 at column 14: Namespace prefix m on semantics is not definederror on line 4 at column 9: Namespace prefix m on mo is not defined

$= 540$ .
Always a multiple of HCF is LCM. In other words, HCF totally divides LCM. Now,

Error parsing MathML: error on line 2 at column 14: Namespace prefix m on semantics is not definederror on line 4 at column 10: Namespace prefix m on mtr is not definederror on line 5 at column 11: Namespace prefix m on mtd is not definederror on line 6 at column 14: Namespace prefix m on mfrac is not definederror on line 8 at column 13: Namespace prefix m on mi is not definederror on line 9 at column 14: Namespace prefix m on mrow is not definederror on line 10 at column 13: Namespace prefix m on mi is not definederror on line 12 at column 11: Namespace prefix m on mo is not definederror on line 13 at column 14: Namespace prefix m on mrow is not definederror on line 14 at column 13: Namespace prefix m on mn is not definederror on line 15 at column 14: Namespace prefix m on mrow is not definederror on line 16 at column 13: Namespace prefix m on mn is not definederror on line 21 at column 10: Namespace prefix m on mtr is not definederror on line 22 at column 11: Namespace prefix m on mtd is not definederror on line 23 at column 28: Namespace prefix m on mfrac is not definederror on line 24 at column 14: Namespace prefix m on mrow is not definederror on line 25 at column 13: Namespace prefix m on mn is not definederror on line 26 at column 12: Namespace prefix m on mn is not definederror on line 31 at column 10: Namespace prefix m on mtr is not definederror on line 32 at column 11: Namespace prefix m on mtd is not definederror on line 33 at column 25: Namespace prefix m on mn is not defined

$L C M of two numbers H C F of tw numbers = 54024 ⇒ 452 ⇒ 22.5 ≠ I n t e g e r$
Hence, two numbers cannot have HCF and LCM as 24 and 540 respectively.
Therefore, the given statement is false.
Thus, option 2 is correct.