Question

LCM and HCF of two numbers are 180 and 3 respectively if one of the two numbers be 45 then the other number will be

Answer 1

Answer:

Given :

• ➞ LCM of two numbers is 180
• ➞ HCF of two numbers is 3.
• ➞ The first number is 45.

$\begin{gathered}\end{gathered}$

To Find :

• ➞ The other number

$\begin{gathered}\end{gathered}$

Concept Used :

• ➞ If 'a' and 'b' are two numbers, then LCM × HCF = a × b

$\begin{gathered}\end{gathered}$

Using Formula :

${\longrightarrow{\small{\underline{\boxed{\sf{LCM \times HCF = Product \: of \: numbers}}}}}}$

• ➟ LCM = Least Common Multiple.
• ➟ HCF = Highest Common Factor
• ➟ Product of numbers = a × b

$\begin{gathered}\end{gathered}$

Solution :

✿ Finding the other number by substituting the values in the formula :

$\begin{gathered}\\ \quad{\longrightarrow{\sf{LCM \times HCF = Product \: of \: numbers}}}\\\\{\longrightarrow{\sf{LCM \times HCF = a \times b}}}\\\\{\longrightarrow{\sf{180 \times 3= 45 \times b}}}\\\\{\longrightarrow{\sf{540= 45 \times b}}}\\\\{\longrightarrow{\sf{b = 540 \div 45}}}\\\\{\longrightarrow{\sf{b = \dfrac{540}{45}}}}\\\\{\longrightarrow{\sf{b = \cancel{\dfrac{540}{45}}}}}\\\\{\longrightarrow{\sf{b = 12}}}\\\\ {\bigstar \: \small{\underline{\boxed{\sf{ \red{Other \: number = 12}}}}}}\end{gathered}$

Hence, the other number is 12.

$\begin{gathered}\end{gathered}$

Verification :

✿ Checking our answer by substituting all values in the formula :

$\begin{gathered}\\ \quad{\longrightarrow{\sf{LCM \times HCF = Product \: of \: numbers}}}\\\\{\longrightarrow{\sf{LCM \times HCF = a \times b}}}\\\\{\longrightarrow{\sf{180 \times 3= 45 \times 12}}}\\\\{\longrightarrow{\sf{540= 540}}}\\\\{\bigstar \: \small{\underline{\boxed{\sf{\red{LHS = RHS}}}}}}\end{gathered}$

Hence Verified!

$\begin{gathered}\end{gathered}$

Learn More :

LCM : The full of LCM is Least Common Multiple. The least number which is exactly divisible by each of the given numbers is called the least common multiple of those numbers.

$\: \: \longrightarrow\rm{LCM = \dfrac{Product \: of \: numbers}{HCF}}$

$\rule{300}{1.5}$

HCF : The full of HCF is Highest Common Factor. The largest number that divides two or more numbers is the highest common factor (HCF) for those numbers. 

$\: \: \longrightarrow\rm{HCF = \dfrac{Product \: of \: numbers}{LCM}}$

$\rule{220pt}{3pt}$

Answer 2

Answer:

lcm=180

hcf=3

first no = 45

second no = x

product of two numbers = hcf×lcm

180×3=45 × x

180×3/45=x

180/15=x

12=x

second no = 12