Question

Find the lcm of 92 and 510 .Also find their hcf by using lcm

Answer 1

Answer:

lcm = 23460, hcf =2

Step-by-step explanation:

use fundamental theorem of arithmetic

it is

lcm × hcf = product of numbers (92,510)

to find hcf use difference method or long division method.

difference method :

find different between numbers 92 and 510 it is 418 it means those two numbers are divided by either 418 or it's factors nothing other than those, by using prime factorization you will get 418= 2×11×19. so 92 and 510 are divided by either 2, 11, 19 or multiplication of any of the 2 out of 3 obtained factors it's either 22, 209, 38 . so as 92 is divided by only 2 out of the 6 factors your hcf is 2.

explanation may be bigger but it's the easiest way to find hcf

long division method :

use Euclid's division algorithm a = bq+r

the smallest of the numbers(92,510) is taken as "a" and other one as dividend

after you get the remainder now put 92 as dividend as remainder is always less than divisor and continue till remainder appears to be zero then the divisor present there is hcf

here it is

92)510(5

460

.....

50)92(1

50

......

42)50(1

42

.....

8)42(5

40

.....

2)8(4

8

...

0

so 2 is hcf so you can find lcm by using fundamental theorem of arithmetic as follows lcm× hcf = product of 92×510 , as we know that hcf is 2 we can find lcm by solving the equation and the lcm is 23460

or

you can directly find lcm by using long division method by taking 2 as factor you get the lcm of 92 and 510 as 23460

here it is

2)92,510

............

46, 255

as there are no common factor between 46 and 255 you will get lcm as 2×46×255=23460 .

using fundamental theorem of arithmetic you will get hcf(92,510) as 2 as mentioned above .