Question

find the greatest 3 digit number exactly divisible by 7 , 9 and 12
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Answer 1

LCM of 7,9,12 = 252

Divide 252 by the greatest 3-digit number, and get the remainder. i.e. 999

-> 999/252 = Remainder = 243

Now, subtract the remainder by 999

-> 999-243 = 756

Hence, the greatest 3 digit number exactly divisible by 7,9, and 12 is 756.

Answer 2

Answer:

The greatest 3 digit number is 756 which is a multiple of 252 and is exactly divisible by  7 , 9 and 12.

Step-by-step explanation:

• Given : Three numbers 7 , 9 and 12

• We need to find out the largest 3-digit number which is exactly divisible by 7 , 9 and 12

• To find out the largest 3-digit number which is exactly divisible by 7 , 9 and 12, we have to calculate the L.C.M 7 , 9 and 12 first.

• L.C.M of 7 , 9 and 12

       7 = 1×7

       9 = 3×3

       12 = 2×2×3

      Hence, the LCM of given numbers 7 , 9 and 12 = 2 x 2 x 3 x 3 x 7 =  

      252

• We have to find the greatest 3 digit multiple of 252 which is exactly divisible by 7 , 9 and 12

• The greatest 3-digit number is 999, I we divide 999 by the obtained LCM that is 252 , we will get the remainder 243.

• 999 ÷ 252 will give the remainder 243.

       Since the remainder is not 0, hence we have to subtract 243 from

       999.

• 999 - 243 = 756 which is a multiple of 252 and is exactly divisible by  7 , 9 and 12.
• Hence, the greatest 3-digit number exactly divisible by  7 , 9 and 12 is 756.

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