To find the Least Common Multiple (LCM) of two numbers, given their Highest Common Factor (HCF), you can use the relationship between the HCF and the LCM of two numbers, which is described by the formula:
[tex]\[
\text{HCF} \times \text{LCM} = \text{Number1} \times \text{Number2}
\][/tex]
Given:
- The HCF (or GCD) of the two numbers is 105.
- The first number [tex]\( \text{Number1} \)[/tex] is 525.
- The second number [tex]\( \text{Number2} \)[/tex] is 630.
Step-by-step solution:
1. Start with the formula that relates HCF and LCM:
[tex]\[
\text{HCF} \times \text{LCM} = \text{Number1} \times \text{Number2}
\][/tex]
2. Substitute the given values into the formula:
[tex]\[
105 \times \text{LCM} = 525 \times 630
\][/tex]
3. Calculate the product of the two numbers:
[tex]\[
525 \times 630 = 330750
\][/tex]
4. Now, to find the LCM, divide the product of the numbers by the HCF:
[tex]\[
\text{LCM} = \frac{330750}{105}
\][/tex]
5. Perform the division:
[tex]\[
\text{LCM} = 3150
\][/tex]
So, the Highest Common Factor (HCF) of the numbers 525 and 630 is 105, and their Least Common Multiple (LCM) is 3150.
