Final answer:
To find the LCM of 15a² and 6w³, factorize both expressions and identify all the common factors. Multiply the common factors together to get the LCM.
Step-by-step explanation:
To find the LCM (Least Common Multiple) of 15a² and 6w³, we need to factorize both expressions. 15a² can be written as 3 * 5 * a * a, and 6w³ can be written as 2 * 3 * w * w * w.
Next, we identify all the common factors between the two expressions: 2, 3, and a². Multiplying all the common factors together gives the LCM: 2 * 3 * a² * 5 * w³.
Simplifying the expression gives the final LCM: 30a²w³.
The student is asking to find the Least Common Multiple (LCM) of the expressions 15a² and 6w³, 30a²w³. To find the LCM of two or more algebraic expressions, we need to identify the highest powers of the variables and the largest numerical coefficient that are present in any of the terms.
The highest power of a is a² (since there is no a term in 6w³), the highest power of w is w³, and the largest numerical coefficient considering all expression is 30 (as in 30a²w³). Therefore, the LCM of the given expressions will be 30a²w³.