math - Number Theory - Factors, HCF and LCM -

30, 40 , 'n' such every number factor of product of other 2 number. if 'n' positive integer , difference between maximum value of 'n' , minimum value of 'n'?

now, since says n factor of product of other 2 numbers, max value n can take 1200 right?

i guess hcf give minimum value of n

listing factors of 30 , 40

30 -> 1,2,3,5,6,10,15,30

40 -> 1,2,4,5,8,10,20,40

hcf(30,40) -> 10

therfore, difference 1200-10 => 1190..

but answer given 1188...where going wrong?

your approach wrong. greatest common divisor of 30 , 40 not smallest n.

you looking smallest integer n > 0 satisfies 40*n = 0 (mod 30) , 30*n = 0 (mod 40).

for first equation, result n_1 = 3. second equation, n_2 = 4. smallest n satisfy both equations least common multiple of n_1 , n_2 -- in case, n = 12.