To find the Least Common Multiple (LCM) of two numbers [tex]\( x \)[/tex] and [tex]\( y \)[/tex], given the product of the numbers [tex]\( xy = 1048 \)[/tex] and their Highest Common Factor (HCF) [tex]\( \operatorname{HCF}(x, y) = 8 \)[/tex], we can use the following relationship between the LCM and HCF of two numbers:
[tex]\[ \operatorname{LCM}(x, y) \times \operatorname{HCF}(x, y) = x \times y \][/tex]
Given:
[tex]\( x \times y = 1048 \)[/tex]
[tex]\( \operatorname{HCF}(x, y) = 8 \)[/tex]
We need to find [tex]\( \operatorname{LCM}(x, y) \)[/tex].
First, substitute the given values into the relationship formula:
[tex]\[ \operatorname{LCM}(x, y) \times 8 = 1048 \][/tex]
Next, solve for [tex]\( \operatorname{LCM}(x, y) \)[/tex] by isolating it on one side of the equation. This can be done by dividing both sides of the equation by 8:
[tex]\[ \operatorname{LCM}(x, y) = \frac{1048}{8} \][/tex]
Now, perform the division:
[tex]\[ \operatorname{LCM}(x, y) = 131 \][/tex]
Thus, the Least Common Multiple (LCM) of the two numbers [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ \operatorname{LCM}(x, y) = 131 \][/tex]
