Home > Practice > Arithmetic Aptitude > HCF & LCM of Numbers > Miscellaneous
1. HCF of 3240, 3600, and a third number is 36 and their LCM is 24 × 35 × 52 × 72 . The third number is = ?
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
Solution:
3240 = 23 × 34 × 53600 = 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