Question

Find the greatest four digit number which is exactly divisible by 18,24,36

Answer 1

Here is a step - by - step procedure to find the greatest four digit number that is exactly divisible by 18,24,36.

1. Find the LCM (Least common multiple) of 18, 24, 36. Any number divisible by the LCM of the 18,24,36 will be divisible by each of 18,24,36.

• To find LCM, write each number as a product of its prime factors.
• 18=3∗3*2———————————————18 has two 3 and one 2
• 24=2∗2∗2∗3———————————24 has three 2’s and one 3.
• 36=2∗2∗3∗3———————————36 has two 2’s and two 3’s.
• To get the LCM: Multiply each factor the greatest number of times it occurs in any of the numbers.
• There are 2 factors : 2,3,
• The greatest number of times 2 occurs in the numbers (18, 24, 36) : three
• The greatest number of times 3 occurs in the numbers (15, 24, 36) : Two
• LCM =2∗2∗2∗3∗3=72

2. To Find the greatest four digit number divisible by 72:

• The greatest four digit number is 9999
• 9999 when divided by 72 is 138.875 ( 138.875 is not an integer, thus 9999 is not divisible by 72. )
• The greatest four digit number divided by 72would be = 72*138=9936

( Note : 138 is the part of the number before the decimal point in 138.875)

3. We can check if 9936 is divisible by each of 18, 24, 36

• 9936/18=552
• 9936/24=414
• 9936/36=276