Finding HCF n LCM of typical values.

Today's concept : Finding HCF n LCM of typical values.

#1 : to find the HCF, LCM quickly.

i know most of us wud know this....if v have few nos., 20,40,50,80,180...to find their LCMs, HCF...there's a slightly quick method...

express them in prime nos.

20 = 2^2 x 5
40 = 2^3 x 5
50 = 5^2 x 2
80 = 2^4 x 5
180 =3^2 x 2^2 x 5

now to HCF, see highest power of all prime nos. that are common to all nos.

2 - 2
3- 0
5 - 1

hence hcf is 2^2 x 5 = 20

to find lcm...see highest power of all prime nos across all nos.

2 - 4
3 - 2
5 - 1

hence, lcm = 2^4 x 3^2 x 5 = 1620.


#2 To find HCF and LCM of the form-

2222....30 times.

3333....70 times.

to solve such questions...

for 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 n 70...thats 10.

so the hcf is 111...written 10 times.

For 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 n 70...thats 210.

so the hcf is 666...written 210 times.

#3...to find hcf and lcm of following form...

2^300 - 1, 8^250 - 1.

the idea is..a^n - b^n is always divisible by a-b. so v need to find highest a-b that will divide a^n - b^n and smallest term that'll be divisible by a^n - b^n.

express them in a common base.

2^300 - 1 and 2^750 -1.

to find hcf...

take hcf of powers i.e. hcf of 300 and 750...i.e. 150

so the hcf is 2^150 - 1.

to find lcm....

take lcm of powers i.e. lcm of 300 and 750...i.e. 1500

so the hcf is 2^1500 - 1.




Questions :

find hcf and lcm of:

1.2222...250 times and 8888...300 times

2. 333....120 times and 1111...400 times

3. 111...700 times and 9999...200 times.

4. HCF of 33333...200 times. and 777777.....300 times

5. 32^250 -1 & 16 ^ 100 - 1.

6. 81^100 -1 & 243 ^ 200 - 1.

7. 343^150-1 & 2401^100 - 1.

8. 125^200 - 1 & 625^120 - 1.

9. 169^320 - 1 & 32^160 - 1.

for the following questns...

mark 1. - stmt 1 is sufficient.
2- stmt 2 is suff.
3-both are reqd to solve the questn.
4-either is suff.
5-both insufficient.

10. what is the hcf of 5 nos., a,b,c,d,e?

stmt 1 - a=72,b=4,c=6
stmt 2 - d= 8, e = 27.

easy set...hope many wud get all correct...