Question

how many number between 400 and 500 are exactly divisible by 12 15 and 20

Answer 1

LCM of 12, 15 and 20 = 60
Now, the numbers between 400 and 500 which are exactly divisible by 60 are 420 and 480.
So the 2 numbers 420 and 480 are exactly divisible by 12, 15 & 20.
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Answer 2

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 * 2

15 =3 * 5

20 = 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

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