HCF of 3240, 3600, and a third number is 36 and their LCM is 2⁴ × 3⁵ × 5² × 7² . The third number is = ?

Explanation:-

3240 = 2³ × 3⁴ × 5
3600 = 2⁴ × 3² × 5²
HCF = 36 = 2² × 3²
Since H.C.F. is the product of lowest powers of common factors, so the third number must have (2² × 3²) as its factors.
Since L.C.M. is the product of highest powers of common prime factors, so the third number must have 3⁵ and 7² as its factors.
∴ Third number = 2² × 3⁵ × 7²