CAT prep online

1) 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.

2) 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 we need to find highest a-b that will divide a^n - b^n (HCF) and smallest term that'll be divisible by a^n - b^n (LCM)

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.

source: pagalguy.com