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7. A drum contained 220 litres of oil and another drum contained 336 litres of oil. What
capacity should the container be to take out the maximum amount of oil from both
the drums at the same time?

Lowest common muLtipLe (Lcm)

Let us take any two numbers, say 4 and 6 and list multiples of 4 and 6.

Multiples of 4 are 4, 8, 12 , 16, 20, 24 , ...
Multiples of 6 are 6, 12 , 18, 24 , ...

Look at the given number line. It shows some multiples of 4 and 6.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Common multiples of 4 and 6 are 12, 24, ... Remember
The lowest common multiple (LCM) of 4 and 6 is 12. When a number is a multiple

Thus, the smallest number which is a multiple of two or more of two or more numbers,
given numbers is called the least common multiple (LCM). then it is called a common
multiple of those numbers.
methods of Finding lcm

We can find the LCM by using any of the three methods:

(i) Common multiples method (ii) Prime factorisation method

(iii) Division method
common multiples method

example 1: Find the LCM of 24 and 32 using the common multiple method.

Solution:
Step 1: Write some multiples of number 24.

Multiples of 24 are 24, 48, 72, 96 , 120, 144, 168, 192, ...
Step 2: Write some multiples of number 32.

Multiples of 32 are 32, 64, 96 , 128, 160, 192, ...
Step 3: List the common multiples of both the numbers.
Common multiples of 24 and 32 are 96, 192, ...

Step 4: The smallest common multiple will be the required LCM.
Thus, the least common multiple (LCM) of 24 and 32 = 96

Prime Factorisation method

Step 1: Express each given number as the product of its prime factors.
Step 2: Take each prime factor as many times as the highest number of times it appear in
the above prime factorisation.

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