Math: HCF and LCM

Type of Problem		Approach to problem
Find The greatest number which is exactly divisible by x, y, z		Required number = HCF of x, y, z
Find The greatest number which is divisible by x, y, z gives reminders a, b, c respectively		Required number = HCF of (x-a), (y-b), (z-c)
Find The least number which is exactly divisible by x, y, z		Required number = LCM of x, y, z
Find The least number which is divisible by x, y, z gives reminders a, b, c respectively		Required number = LCM of (x-a), (y-b), (z-c)
Find The least number which is divisible by x, y, z  gives reminders ‘r’		Required number = LCM of (x, y, z)+r
Find The least number which is divisible by x, y, z  gives same reminders		Required number = HCF of (x-y), (y-z), (z-x)
Find the n digits Greatest number which is divisible by x, y, z		LCM  of x, y, z =L Divide the n-digits greatest number by L and reminder R Leaves No Reminder then: N digit number – R Leaves reminder K in each case [n digit number –R] + k
Find the n digits Smallest number which is divisible by x, y, z		LCM  of x, y, z =L Divide the n-digits greatest number by L and reminder R Leaves No Reminder then: Required number: n digit smallest number + (L-R) Leaves reminder K in each case Required number: n digit smallest number+(L-R)+K