 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.

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.

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,
$\dfrac{12\times 240}{48}=x$
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,
$\therefore x=\dfrac{\dfrac{12\times 240}{12}}{\dfrac{48}{12}}$
Further simplification in the above equation will give,
$\therefore x=\dfrac{240}{4}$
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.