Answer:
The LCM of 40 and 150 is 600.
Explanation:
To find the Least Common Multiple (LCM) of 40 and 150, you can use the prime factorization method.
Find the prime factorization of each number:
For 40: 40 = 2^3 * 5
For 150: 150 = 2 * 3 * 5^2
Identify all the prime factors that appear in either of the numbers and their highest powers:
The common prime factors are 2, 3, and 5.
The highest power of 2 is 3 (from 2^3).
The highest power of 3 is 1 (from 3).
The highest power of 5 is 2 (from 5^2).
Multiply these highest powers of the common prime factors:
LCM = 2^3 * 3^1 * 5^2
Calculate the LCM:
LCM = 8 * 3 * 25
Now, multiply these numbers together to find the LCM:
LCM = 8 * 3 * 25 = 600
So, the LCM of 40 and 150 is 600.