Question

Two cans contain 60 and 135
litres of milk respectively. Find a
can of maximum capacity which
can measure the milk in both the
cons​

Answer 1

Answer:

• Maximum capacity of a can to measure the milk in the both cans is 15 litres.

Step-by-step explanation:

Given that:

• Two cans contain 60 and 135 litres of milk respectively.

To Find:

• A can of maximum capacity which can measure the milk in both the cans.

Concept:

• For finding a can of maximum capacity which can measure the milk in both the cans, we have to find the HCF of 60 and 135 after that we will get a can of maximum capacity.

Finding the HCF of 60 and 135:

By prime factorisation.

⇒ Factor of 60 = 2² × 3 × 5

⇒ Factor of 135 = 3³ × 5

Common factors of 60 and 135 is (3 × 5).

Hence, The HCF of 60 and 135 is 15.

We get that:

• A can of 15 litres capacity can measure the milk in both the cans.

Answer 2

${\bf{Given\::}}$

• Two cans contain 60 litres and 135 litres of milk respectively.

$\\ {\bf{To\: Find\::}}$

• The maximum capacity of a can which can measure the milk of each can when used an exact number of times.

$\\ {\bf{Solution\::}}$

☛ To calculate maximum capacity of a can that measures the milk in exact number of times, we need to find H.C.F of 60 & 135.

⠀⠀⠀ $\red\star$ H.C.F of 60 & 135 $\red\star$

${\begin{array}{r | l} 2 & 60 \\ \cline{2-2} 2 & 30 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} & 5 \end{array}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: {\begin{array}{r | l} 3 & 135 \\ \cline{2-2} 3 & 45 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} & 5 \end{array}}$

➠ 60 = 2 × 2 × 3 × 5

➠ 135 = 3 × 3 × 3 × 5

✯ H.C.F of 60 & 135 = 3 × 5 = 15

Hence,

$\dashrightarrow\:\:\bf{Max^m~ capacity~ of~ the~ can~ =~ H.C.F ~of ~60~ \& ~135~}$

$\dashrightarrow\:\:\bf\pink{Max^m~ capacity~ of~ the~ can~ =~ 15~L}$

∴ The maximum capacity of the can is 15 L.