Question

find the sum of all positive integers less than 250 that are divisible by both 3 and 4​

Answer 1

Answer:

Step-by-step explanation:

last number less than 250 divisible by 3 is 249

last number less than 250 divisible by 4 is 248.

first divisible by 3 is 3.

first number divisible by 4 is 4.

sum of numbers from 3 to 249

There are 83 such numbers between 3 and 249 divisible by 3.

sum=83(6+(82)*3)/2

=10458

sum of numbers from 4 to 248

There are 62 such numbers between 4 and 248 divisible by 4.

sum=62(8+(61)*4)/2

=7812

sum=10458+7812=18270

The numbers 12,24 ..... numbers divisible by 12 have been repeated twice

so sum of all numbers divisible by 12 less than 250 is

12,24,.....240

There are 20 such numbers.

sum of 12=20(24+19*12)/2=1260

Final sum = 18270-1260

=17010

Answer 2

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