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## HCF & LCM Notes & Questions

This topic will cover all the Tricks for **HCF(Highest Common Factors) and LCM(Lowest Common Multiple)**.** **Some formula is given below in details and proper use of the formula to illustrate and make you understand well. Candidates preparing for **bank exam (Clerk,PO,SO)** and can also download these notes in **PDF** format.

### What is HCF (Highest Common Factors)-म०स०प०

HCF is that integers numbers which divide the number.The highest common factor of two or more given numbers is the largest of their common factors.It is also known as GCD (Greatest Common Divisor).

### What is LCM(Lowest Common Multiple)-ल०स०प०

LCM is the number which is multiple of two or more numbers.The least common multiple of two or more given numbers is the least of their common multiples.

Following are the HCF & LCM questions and HCF & LCM shortcut tricks that will help you to pass IBPS clerk and IBPS PO,thus getting a good IBPS result.

### Formula for HCF & LCM

- Product of two numbers = HCF * LCM.
- HCF of given numbers always divides LCM.
- HCF =
^{ } - LCM =
^{ } - If d is the h.c.f. of two positive integer a and b, then there exist unique integer m and n, such that d=am+bn.
- Largest number which divides x,y,z to leave same remainder = HCF of y-x, z-y, z-x.
- Largest number which divides x,y,z to leave remainder R (i.e. same) = HCF of x-R, y-R, z-R.
- Largest number which divides x,y,z to leave same remainder a,b,c = HCF of x-a, y-b, z-c.
- Least number which when divided by x,y,z and leaves a remainder R in each case = ( LCM of x,y,z) + R.

### HCF & LCM of fractions

HCF of fraction =

LCM of fraction =^{LCM of Numerators}⁄_{HCF of Denominators}