1. How many numbers between 400and 500 are exactly divisible by 12,15

1.	1. How many numbers between 400and 500 are exactly divisible by 12,15 and 20?(a) One(c) Three(b) Two(d) of these
Answer» if a number is divisible by 12 15 and 20 then it is divisible by LCM of these 3 LCM of 12 15 and 20 can be computed by factorisation 12 = 3 * 2 * 215 =3 * 520 = 5 * 2 * 2 si\o LCM = 3 * 22 5 (higest power of each prime in each number)= 60 so the number is divisible by 60 now 2 multiles of 60 607 and 60*8 are between 400 and 500 so number of numbers = 2 right thanks

1. How many numbers between 400and 500 are exactly divisible by 12,15 and 20?(a) One(c) Three(b) Two(d) of these

Answer»

if a number is divisible by 12 15 and 20 then it is divisible by LCM of these 3

LCM of 12 15 and 20 can be computed by factorisation

12 = 3 * 2 * 215 =3 * 520 = 5 * 2 * 2

si\o LCM = 3 * 2*2* 5 (higest power of each prime in each number)= 60

so the number is divisible by 60

now 2 multiles of 60 *60*7 and 60*8 are between 400 and 500 so number of numbers = 2

right

thanks