What is the LCM of 14 and 35? a. 140 b. 70 c. 56 d. 7
2 answers:
Answer: 70
Step-by-step explanation: To find the least common multiple for the integers 14 and 35, we start by making a factor tree for each of the integers.
14 factors as 2 × 7 and 35 is 7 × 5. We are looking for the factors that match up.
In this case, both integers have a factor of 7.
When finding the LCM, we multiply all the factors together, but because the 7's match up, we only need to multiply by 7 once.
So we have 2 × 7 × 5 which is 70.
Therefore, the least common multiple for 14 and 35 is 70.
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Equation 1: 
Equation 2:
We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.
In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method
We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same
Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2
To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10
Equation 1: Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x
Equation 1:
Equation 2:
Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)
Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80
Hence the correct answer is: Third option
Equation 2:
We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.
In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method
We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same
Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2
To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10
Equation 1: Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x
Equation 1:
Equation 2:
Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)
Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80
Hence the correct answer is: Third option