Examveda
Examveda

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

A. 22 × 35 × 72

B. 22 × 53 × 72

C. 25 × 52 × 72

D. 23 × 35 × 72

Answer: Option A

Solution(By Examveda Team)

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

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