Find the LCM for the given numbers by an appropriate method. 135, 56, and 150
Factor each term into the smallest numbers to find the LCM (Least Common Multiple)..
135 = 5 * 3 * 3 * 3
Do the same for the other two numbers and take your pick.
210
To find the least common multiple (LCM) of the given numbers, we can use the prime factorization method. Here's how you can do it step by step:
1. Begin by writing the prime factorization of each number:
- 135: 3 * 3 * 3 * 5
- 56: 2 * 2 * 2 * 7
- 150: 2 * 3 * 5 * 5
2. Now, list all the unique prime factors with their highest exponent:
- 2^3, 3^3, 5^2, 7^1
3. Multiply these prime factors together:
2^3 * 3^3 * 5^2 * 7^1 = 8 * 27 * 25 * 7 = 37,800
Therefore, the least common multiple (LCM) of 135, 56, and 150 is 37,800.
Alternatively, if you prefer using another method, you can also find the LCM by listing the multiples of the numbers and finding the least common multiple. However, the prime factorization method is generally more efficient, especially for larger numbers.