Question

The LCM of 248 and 868 is 1736, then their HCF is
A) 142
B) 124
C) 421
D) 241

Answer 1

Hint:
Here, we will use the formula that the product of two numbers is equal to the product of their HCF and LCM. Substituting the given values in the formula, we will get the required value of the HCF of the given two numbers.

Formula Used:
\[L.C.M. \times H.C.F. = m \times n\]

Complete step by step solution:
The given two numbers are: 248 and 868
The L.C.M. of two numbers is 1736.
Let us assume that the H.C.F. of the two numbers is \[x\].
We know that the product of two numbers is equal to the product of their LCM and HCF.
Substituting \[L.C.M = 1736\], \[m = 248\] and \[n = 868\] in the formula \[L.C.M. \times H.C.F. = m \times n\], we get
\[1736 \times x = 248 \times 868\]
Dividing both sides by 1736, we get
\[ \Rightarrow x = \dfrac{{248 \times 868}}{{1736}}\]
Simplifying the expression, we get
\[ \Rightarrow x = \dfrac{{248}}{2}\]
Dividing 248 by 2, we get
\[ \Rightarrow x = 124\]
Therefore, the H.C.F. of the given two numbers is 124.

Hence, option B is the correct answer.

Note:
Least Common Multiple or LCM is the smallest possible common multiple of any given natural numbers.
Highest Common Factor or HCF is the largest common factor of two or more given numbers. Now, we have seen the property of LCM and HCF which is:\[{\rm{L}}{\rm{.C}}{\rm{.M}}{\rm{.}} \times {\rm{H}}{\rm{.C}}{\rm{.F}}{\rm{.}} = m \times n\]
Now, this property is applicable for only two numbers.
Also, HCF of any given numbers can never be greater than those numbers and LCM of any given numbers can never be smaller than those numbers.