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7. A drum contains 220 litres of oil and another drum contains 336 litres of oil. Find the
largest capacity of a container that can exactly measure the oil from both drums.

Critical Thinking
Challenge Question
A farmer plans to plant apple trees, orange trees, and mango
trees in rows such that each row contains only one type of

tree and has the same number of trees. The farmer has 132
apple trees, 176 orange trees, and 264 mango trees.
Find the greatest number of trees that can be planted in
each row. Determine how many rows will be needed in total.

Lowest common muLtipLe (Lcm)

Let us take any two numbers, say 4 and 6 and list the 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, ...
Math Insight
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
Methods of Finding lcM multiple of those numbers.

We can find the LCM 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 multiples method.
Solution:

Step 1: Write some multiples of the number 24.
Multiples of 24 are 24, 48, 72, 96 , 120, 144, 168, 192, ...

Step 2: Write some multiples of the number 32.
Multiples of 32 are 32, 64, 96 , 128, 160, 192, ...

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