Question

Find sum of all 3 digit numbers which are divisible by 72, 80 and 120

Answer 1

LCM of 72 , 80 , 120 (÷ 2 )

= 36 , 40 , 60 (÷ 2)
= 18 , 20 , 30 (÷ 2)
= 9 10 15 (÷ 3 )
= 3 10 5 (÷ 5)
= 3 2 1

LCM = 720

: there's only 1 number that is 720 becoz 720's multiple are of 4-digit.

Answer 2

The sum of all 3 digit numbers which are divisible by 72 , 80 and 120 is 720

Given :

The numbers 72 , 80 and 120

To find :

The sum of all 3 digit numbers which are divisible by 72 , 80 and 120

Solution :

Step 1 of 4 :

Write down the given numbers

The given numbers are 72 , 80 and 120

Step 2 of 4 :

Prime factorise the given numbers

72 = 2 × 2 × 2 × 3 × 3

80 = 2 × 2 × 2 × 2 × 5

120 = 2 × 2 × 2 × 3 × 5

Step 3 of 4 :

Find the LCM

We know that the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

LCM of 72 , 80 and 120

= 2 × 2 × 2 × 2 × 3 × 3 × 5

= 720

Step 4 of 4 :

Find the required sum

720 × 1 = 720

720 × 2 = 1440

So 720 is the only 3 digit numbers which is divisible by 72 , 80 and 120

Hence the required sum of all 3 digit numbers which are divisible by 72, 80 and 120 is 720

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