Question

Problem How many four digit positive
integers are divisible by both 12 and 20, but are not divisible by 16 ?​

Answer 1

Given :   four-digit positive integers are divisible by both 12 and 20, but are not divisible by 16

To Find : How many four-digit positive integers are divisible by both 12 and 20, but are not divisible by 16

Solution:

Number divisible by both 12 and 20

=> Number divisible by  LCM of 12 & 20

12 = 2 * 2 * 3

20 = 2 * 2 * 5

LCM = 2 * 2 * 3 * 5  = 60

but are not divisible by 16  

LCM of 60 and 16   =  240  

4 Digit numbers 1000  to    9999

Divisible by 60

1020  , 1080 ,____________,  9960

17 * 60  , 18 * 60 __________166 * 60

Hence total numbers = 166 - 17 + 1  = 150

Divisible by 240

1200  , 1440 ,____________,  9840

5 * 240  , 6 * 240 __________41 * 240

Hence total numbers = 41- 5 + 1  =37

four-digit positive integers are divisible by both 12 and 20, but are not

divisible by 16 = 150 - 37  = 113

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