Question

Q . n is a natural number such that the least common multiple of n and 72 is 360.
Find the average of all possible values of n between 52 and 98, which satisfy the above
condition.
please tell me the answer
# needed with explanation
# no spamming plz​

Answer 1

Answer:

average = 75

Step-by-step explanation:

only 60 & 90 b/w 52&98 satisfy the condition.

LCM of 60 & 72 is 360

& LCM of 90& 72 is 360

explanation:

360=2x2x2x3x3x5=72x5

in "n" 5 is required & all other factors of n must be common with the factors of 72, so by multiplying 5 with the factors of 72(2x2x2x3x3) we get different numbers

5x2=10

5x2x2=20

5x2x2x2=40

5x2x2x2x3=120

5x2x2x2x3x3=360

5x2x2x3x3=180

5x2x2x3=60

5x2x3x3=90

here only 60 & 90 lies b/w 52&98.

now the average of 60&90 is (60+90)/2=75

maybe this will help u.

thanks