What are the place values of the digits 1 and 0 in 2013, and what is the LCM of 18 and 12?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: Place Value

To find the place value of the digits 1 and 0 in the number 2013:

The place value of 1 is $\boxed{\text{tens}}$ .
The place value of 0 is $\boxed{\text{hundreds}}$ .

: Lowest Common Multiple (LCM)

The prime factors of 18 and 12 are given as:

18 = 2 \times 3^2

12 = 2^2 \times 3

Identify all unique prime factors from both numbers.
The unique prime factors are 2 and 3.
For each prime factor, take the highest power that appears in either factorization.
- For the prime factor 2: The powers are $2^1$ (from 18) and $2^2$ (from 12). The highest power is $2^2$ .
- For the prime factor 3: The powers are $3^2$ (from 18) and $3^1$ (from 12). The highest power is $3^2$ .
Multiply these highest powers together to find the LCM.
$\text{LCM}(18, 12) = 2^2 \times 3^2$ $\text{LCM}(18, 12) = 4 \times 9$ $\text{LCM}(18, 12) = 36$
The lowest common multiple (LCM) of 18 and 12 is $\boxed{36}$ .

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