Find the LCM for the following Terms; 12X3Y, 6X2 Y3, 18X4Y2
the 2s and 3s are squared
a. 36X3 Y2
b. 72X4Y
c. 36X4Y3
d. 108X4Y3
To find the LCM (Least Common Multiple) for the given terms 12X3Y, 6X2Y3, and 18X4Y2, we need to find the highest power of each variable that appears in any of the terms.
For the variable X, the highest power among the terms is 4 (from 18X4Y2).
For the variable Y, the highest power among the terms is 3 (from 6X2Y3).
Now, we need to consider the coefficients (numbers in front of the variables).
For the coefficient 12, it is divisible by 6 and 18.
For the coefficient 6, it is divisible by 6.
For the coefficient 18, it is not divisible by either 6 or 12.
To find the LCM of the coefficients, we take the highest divisible number as the LCM, which is 18.
Therefore, the LCM of the coefficients is 18.
Now, let's combine the LCM of the coefficients (18) with the highest powers of each variable:
a. 36X3Y2: This answer is not correct. The coefficient is incorrect. The correct answer should be 18X3Y2.
b. 72X4Y: This answer is correct.
c. 36X4Y3: This answer is not correct. The coefficient is incorrect. The correct answer should be 18X4Y3.
d. 108X4Y3: This answer is correct.
So, the correct answers are:
b. 72X4Y
d. 108X4Y3