Question

Find the HCF of 867 and 225 by eculid division algorithm HCF and LCM

Answer 1

Answer:

HCF

By Euclid's Division Lemma ,

a = bq +r , where remainder is equal to 0 or greater than 0 but less than b.

a= Dividend

b = divisor

q = quotient

r = remainder

As 867 is greater than 225 so we will divide 867 by 225 .

867 = 225 × 3 + 192

225 = 192 × 1 + 33

192 = 33 × 5 + 27

33 = 27 × 1 + 6

27 = 6 ×4 + 3

6 = 3 × 2 + 0

The remainder has became 0 , so the Hcf of 867 and 225 is 3 .

LCM

Lcm = product of greatest power of prime factors

$867 = 3 \times 17 { }^{2} \\ 225 = 3 {}^{2} \times 5 {}^{2}$

So the lcm is :

$17 {}^{2} \times 3 {}^{2} \times 5 {}^{2} \\ = 65025$