HCF & LCM SHORT TRICKS HCF (Highest Common factor) There are two methods to find the HCF– (a) Factor method (b) Division ...
HCF & LCM SHORT TRICKS
There are two methods to find the HCF–
(a) Factor method (b) Division method
(i) For two no. a and b if a < b, then HCF of a and b is always less than or equal to a .
(ii) The greatest number by which x, y and z completely divisible is the HCF of x, y and z.
(iii) The greatest number by which x, y, z divisible and gives the remainder a, b and c is the HCF of (x –a), (y–b) and (z–c).
(iv) The greatest number by which x, y and z divisible and gives same remainder in each case, that number is HCF of (x–y),(y–z) and (z–x).
LCM (Least Common Multiple)
There are two methods to find the LCM–
(i) For two numbers a and b if a < b, then L.C.M. of a and b is more than or equal to b.
(ii) If ratio between two numbers is a : b and their H.C.F. is x, then their L.C.M. = abx.
(iv) The smallest number which is divisible by x, y and z is L.C.M. of x, y and z.
(v) The smallest number which is divided by x, y and z give remainder a, b and c, but (x – a) = (y – b) = (z – c) = k, then numberis (L.C.M. of (x, y and z) – k).
(vi) The smallest number which is divided by x, y and z give remainder k in each case, then number is (L.C.M. of x, y and z) + k.
(viii) For two numbers a and b –LCM × HCF = a × b
COMMENTS