# FIND THE GREATEST 3 DIGIT NUMBER DIVISIBLE BY THE GIVEN NUMBERS

Purpose of finding LCM :

By finding the least common multiple, we will get the number which will be the multiple of given numbers. Or the value that we find will be divisible by the given numbers.

Step 1 :

Find the least common multiple of given numbers.

Step 2 :

Select the greater number, for example

• the greater 3 digit number is 100
• the greater 4 digit number is 1000.

Step 3 :

Divide the values by the least common multiple, then the dividend should be subtracted with the remainder. And the result is the greatest number which is divisible by the given numbers.

Problem 1 :

Determine the greatest 3 digit number which is exactly divisible by 6, 8 and 12.

Solution :

By finding the least common multiple of 6, 8 and 12

LCM (6, 8 and 12) = 24

By dividing 1000 (least four digit number) by 24, we get

1000 - 16 ==> 984

So, 984 is the greatest 3 digit number which is divisible by 24.

Problem 2 :

Find the greatest 3 digit number exactly divisible by 8, 10 and 12.

Solution :

LCM (8, 10 and 12) = 120

1000 - 40 ==> 960

So, 960 is greatest 3 digit number which is divisible by 120.

Problem 3 :

Find the greatest 4 digit number which is divisible by 18, 24 and 32.

Solution :

LCM (18, 24 and 32)

LCM = 288

The greatest 5 digit number is 100000.

10000 - 208 ==> 9792

So, 9792 is the greater four digit number divisible by 18, 24 and 32.

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