Math, asked by yash123495, 1 year ago

HCF and LCM of 17 102 170

Answers

Answered by niraj1219pc1cuv

hcf of 17 102 and 170 is 17.
LCM = 510

Answered by Laxmipriyas007

Answer:

HCF is 17 and LCM is 510.

Step-by-step explanation:

To Find: LCM (Lowest Common Multiple) and HCF (Highest Common Factor)

Use Prime Factorization.

First, decompose the numbers into their prime factors:

17 is prime, so 17 = 17

To decompose 102:

$\frac{102 }{ 2}$ = 51,

$\frac{51 }{ 3}$ = 17.

17 is prime, thus 102 = 2 x 3 x 17

To decompose 170:

$\frac{170 }{ 2}$ = 85,

$\frac{85 }{ 5}$ = 17.

17 is prime, thus 170 = 2 x 5 x 17.

The LCM can be found by multiplying together the highest powers of all bases. The bases (primes that the numbers were decomposed into) are all to the power 1, so nothing to worry about there. All the bases we have are 2, 3, 5, and 17. Therefore, the LCM = 2 x 3 x 5 x 17 = 510.

The HCF can be found by multiplying together the lowest bases of common bases. The only bases that are common between all numbers are 17, therefore the HCF = 17.