Question

The 5 digit greatest number which is divisible by 12.18 and 24
(a) 99996
(b) 99972
(c) 99936
(d) 99960
​

Answer 1

To Find:

• The 5 digit greatest number which is divisible by 12, 18 and 24.

Finding the LCM of 12, 18 and 24:

By prime factorisation.

• Factors of 12 = 2² × 3
• Factors of 18 = 2 × 3²
• Factors of 24 = 2³ × 3

LCM (12, 18 and 24) = 2³ × 3² = 72

We have:

• LCM of 12, 18 and 24 = 72
• 5 digit greatest number = 99999

Dividing 99999 by 72.

• 99999 = 72 × 1388 + 63

Quotient = 1388 and Remainder = 63

Subtracting 63 from 99999.

• 99999 - 63 = 99936

Hence,

• The 5 digit greatest number which is divisible by 12, 18 and 24 is (c) 99936.

Answer 2

Given :-

Three number - 12,18 and 24

To Find :-

Greatest 5 digit number

Solution :-

Before solving the question we have to first find out the LCM of 12, 18 and 24 and then we will divide the LCM by the greatest 5 digit number and afterwards the remainder will be subtracted from the greatest 5 digit number

Let's solve

Greatest 5 digit number = 99999

Now

Multiple of 12 = 12,24,36,48,60,72,84

Multiple of 18 = 18,36,54,72,90

Multiple of 24 = 24,48,72,96

LCM = 72

Now

$\sf 72)99999(1388 \; and \; remainder \; is \; 63$

Subtracting

99999 - 63 =  99936