## Problems on H.C.F and L.C.M

H.C.F and L.C.M Practice different types of aptitude test , including numerical and verbal tests. All questions come with worked solutions

### What is H.C.F and L.C.M ?

**HCF is the greatest common divisor of more than oneÂ integers. Hence, the largest positive integer that divides more than oneÂ integers known as Highest common factor.LCM is the least common multiple of two or more integers.**

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Here, are some easy tips and tricks for you to solve HCF and LCM questions quickly, easily, and efficiently in competitive exams.

### H.C.F and L.C.M Tips and Tricks and Shortcuts

- The H.C.F of two or more numbers is smaller than or equal to the smallest number of given numbers
- The smallest number which is exactly divisible by a, b and c is L.C.M of a, b, c.
- The L.C.M of two or more numbers is greater than or equal to the greatest number of given numbers.
- The smallest number which when divided by a, b and c leaves a remainder R in each case.
**Required number = (L.C.M of a, b, c) + R** - The greatest number which divides a, b and c to leave the remainder R is
**H.C.F of****(a â€“ R)**,**(b â€“ R)**and**(c â€“ R)** - The greatest number which divide x, y, z to leave remainders a, b, c is
**H.C.F of (x â€“ a), (y â€“ b)**and**(z â€“ c)** - The smallest number which when divided by x, y and z leaves remainder of a, b, c (x â€“ a), (y â€“ b), (z â€“ c) are multiples of M
**Required number = (L.C.M of x, y and z) â€“ M**