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The HCF and LCM of two numbers are 15 and 270.

Find the LCM of the numbers 525 and 630, given that their HCF is 105.

The LCM of numbers 48 and 60 is 240.

Find the HCF.

Sagot :

GinnyAnsweridn
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]
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