## LCM and HCF tricks, problems and formulas

For example: The common multiples of 3 and 4 are 12, 24 and so on. Therefore, LCM is smallest positive number that is multiple of both. Here, LCM is 12.

HCF i.e. Highest Common Factor are those integral values of number that can divide that number. LCM and HCF problems are very important part of all competitive exams.

## Some important LCM and HCF tricks:

1) Product of two numbers = (HCF of numbers) x (LCM of numbers)

2) HCF of given numbers always divides their LCM

3) HCF of given fractions = HCF of numerator / LCM of denominator

4) LCM of given fractions = __ LCM of numerator / HCF of denominator__

5) If d is the HCF of two positive integer a and b, then there exist unique integer m and n, such that

d = am + bn

6) If p is prime and a,b are any integer then __P (ab )__

**,**this implies

__P(a )__or

__P(b)__

7) HCF of a given number always divides its LCM

#### Least number which when divided by 5,6,7,8 and leaves remainder 3, but when divided by 9, leaves no remainder?

#### Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

#### The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

#### Find the lowest common multiple of 24, 36 and 40.

#### The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

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