HCF and LCM

Hi folks, today we are going to learn HCF and LCM. Every year you would invariably find problems on HCF and LCM in CAT, and believe me its one of the most scoring section ignored by students preparing for CAT, GMAT or any other competitive exam.

I wont tell you how to find HCF and LCM (although I have few shortcuts on them but I believe you would be knowing it by now, still if you want you can mail me).

Here are a few tips and tricks.

• HCF will be lesser than or equal to the least of the numbers and LCM will be greater than or equal to the greatest of the numbers. (most important to distinguish when to apply when)

• The H.C.F is the greatest number that exactly divides all the given numbers.

• The least number which is divisible by each one of given numbers is LCM.

• LCM of fraction= LCM of numerators / HCF of denominators

• HCF of fraction= HCF of numerator / LCM of denominators

• For two numbers, the product of numbers = HCF × LCM (mostly useless nowadays)

• While calculating HCF or LCM of fractions, the fractions should be in the most reducible form. (shed as much blood as you can)

One more trick,

To find HCF and LCM of the form- 2222....30 times and 3333....70 times (any random numbers)

HCF Take hcf of no. thats being repeated...i.e. hcf of 2 & 3. i.e. 1 Take hcf of no. of time these nos. are being repeated i.e. hcf of 30 and 70 is 10. So the hcf is 1...written 10 times. LCM Take lcm of no. thats being repeated...i.e. lcm of 2 & 3. i.e. 6 Take lcm of no. of time these nos. are being repeated i.e. lcm of 30 and 70 is 210. So the hcf is 6...written 210 times.

Now try these problems,

1.The HCF of 2 numbers is 84 and LCM is 95.If one of numbers is 7.find other unit digit of other. (must be solved within 3 seconds)

2.Find least number which when divided by 20,25,35,40 leaves remainders 14,19,29,34.

3.Find the numbers if, the sum of two numbers is 216 and HCF is 27.

4.Which is greatest 1/2,1/3,1/4,5/6,7/8,9/11?

5.What is the smallest number when divided by 2,3,5,6, gives remainder 1. (Tricky)

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That's it folks hope you learned something out of this, until next time if you have any queries then mail me at friggere.Sumit@gmail.com. Bye.