Question

The HCF and LCM of two numbers are 12 and 240 respectively. If one of the numbers is 48 then find the other number.

Answer 1

Hint: Assume the other number as ‘x’ and then use the formula “Highest Common Factor (HCF) $\times$ Lowest Common Multiple (LCM) = Product of two numbers” and substitute the given values in the formula to get the final answer.

Complete step-by-step answer:
To solve the above question we will write the given data first, therefore,
Highest Common Factor (HCF) = 12 ……………………………………………………… (1)
Lowest Common Multiple (LCM) = 240 …………………………………………………. (2)
One of the number = 48 ………………………………………………………………………… (3)
Now we will assume the another number ‘x’ therefore,
Another number = x ………………………………………………………………………… (4)
Now to find the another number we should know the important property of Highest Common Factor (HCF) and Lowest Common Multiple (LCM) which is given below,
Formula: (Property)
Highest Common Factor (HCF) $\times$ Lowest Common Multiple (LCM) = Product of two numbers
If we put the values of equation (1), equation (2), equation (3) and equation (4) in the above formula we will get,
 Therefore, 12 $$\times$$ 240 = 48 $$\times$$ x
If we shift 48 on the left hand side of the equation we will get,
${\displaystyle \frac{12\times 240}{48}}=x$
By rearranging the above equation we will get,
$\therefore x=60$
If we divide both numerator and denominator of the above equation by 12 we will get,
$\therefore x={\displaystyle \frac{{\displaystyle \frac{12\times 240}{12}}}{{\displaystyle \frac{48}{12}}}}$
Further simplification in the above equation will give,
$\therefore x={\displaystyle \frac{240}{4}}$
If we divide 240 by 4 in the above equation we will get,
Therefore, x = 60
If we compare the above equation with equation (4) we will get,
Therefore, another number = 60
Therefore the two numbers having Highest Common Factor (HCF) and Lowest Common Multiple (LCM) equal to 12 and 240 respectively are 48 and 60.

Note: The formula “Highest Common Factor (HCF) $\times$ Lowest Common Multiple (LCM) = Product of two numbers” is very much important while solving this problem. Without it you will keep struggling to find the answer but you won’t be able to get it.