Certainly! Let's go through the step-by-step solution.
### Part 1: Finding the LCM of 525 and 630
We are given:
- [tex]\( \text{HCF}(525, 630) = 105 \)[/tex]
To find the LCM of two numbers, we use the relationship between HCF (Highest Common Factor) and LCM (Least Common Multiple):
[tex]\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \][/tex]
Here, [tex]\( a = 525 \)[/tex] and [tex]\( b = 630 \)[/tex].
[tex]\[ \text{LCM}(525, 630) = \frac{525 \times 630}{105} \][/tex]
Carrying out the division and multiplication:
[tex]\[ 525 \times 630 = 330750 \][/tex]
[tex]\[ \frac{330750}{105} = 3150 \][/tex]
So, the LCM of 525 and 630 is [tex]\( 3150 \)[/tex].
### Part 2: Finding the LCM of 48 and 60
We are given:
- [tex]\( \text{LCM}(48, 60) = 240 \)[/tex]
Since we are directly provided with the LCM for 48 and 60, there is no need for further calculation. The LCM of 48 and 60 is [tex]\( 240 \)[/tex].
### Summary
- The LCM of 525 and 630 is [tex]\( 3150 \)[/tex].
- The LCM of 48 and 60 is [tex]\( 240 \)[/tex].
Thus, the final answers are:
[tex]\[
\text{LCM}(525, 630) = 3150
\][/tex]
[tex]\[
\text{LCM}(48, 60) = 240
\][/tex]
