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6. The L.C.M. of two numbers is 120 and their H.C.F. is 6. If one of the numbers is 12, find the other number.

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To find the other number given the L.C.M. (Least Common Multiple) and H.C.F. (Highest Common Factor) of two numbers, we can use the relationship between the L.C.M. and H.C.F. of two numbers, which is expressed as:

[tex]\[ \text{LCM} \times \text{HCF} = \text{Number1} \times \text{Number2} \][/tex]

Given:
- LCM = 120
- HCF = 6
- Number1 = 1324

We need to find Number2. We can rearrange the formula to solve for Number2:

[tex]\[ \text{Number2} = \frac{\text{LCM} \times \text{HCF}}{\text{Number1}} \][/tex]

Substitute the given values into the formula:

[tex]\[ \text{Number2} = \frac{120 \times 6}{1324} \][/tex]

Calculate the numerator:

[tex]\[ 120 \times 6 = 720 \][/tex]

Now, compute the division:

[tex]\[ \text{Number2} = \frac{720}{1324} \][/tex]

When we perform this division, we get:

[tex]\[ \text{Number2} = 0 \][/tex]

Therefore, the other number is 0.
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