Since x, 2x, 3x contain numbers and variables, it takes two steps to find the LCM. Find the LCM for the numerical part 1; 2; 3; then find the LCM for the variable part x¹ ; x¹; x¹.
The LCM is the smallest number by which all numbers are divided without leaving a remainder.
- List the prime factors of each number.
- Multiply each factor the greatest number of times that occurs in any of the numbers.
The number 1 is not a prime number because it only has one positive factor, which is itself.
not cousin.
Since 2 has no divisors other than 1 and 2.
2 is a prime number.
Since 3 has no divisors other than 1 and 3.
3 is a prime number.
The least common multiple LCM of 1,2,3 is the result of multiplying all the prime factors the greatest number of times that appear in each term.
2 × 3
Multiply 2 by 3.
6
The factor for x¹ is x itself.
x¹ = x
The Least Common Multiple LCM of x¹ ; x¹; x¹ is the result of multiplying all the prime factors the greatest number of times that appear in each term.
x
The LCM for x;2x;3x is the numerical part 6 multiplied by the variable part.
6x ====> Answer
A suitable calculator finds the determinant to be ...
... B. -203
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This can be calculated by hand by copying the first two columns to the right of the given matrix, then forming the sum of products of the downward diagonals and subtracting the sum of products of the upward diagonals.
... (-4)(3)(-5) +(-4)(-5)(-5) +(-3)(3)(2) -(-5)(3)(-3) -(2)(-5)(-4) -(-5)(3)(-4)
... = 60 -100 -18 -45 -40 -60
... = -203
