Find the LCM for the given numbers by an appropriate method. 135, 56, and 150.
Which method is the most appropriate?
135 56 150
divide by 5 27 56 30
divide by 3 9 56 10
divide by 2 9 28 5
so the LCM is 5 x 3 x 2 x 9 x 28 x 5
= 37800
Where did you get the numbers to divide by from?
you gotto look at he numbers at hand
if it ends in a 5 or 0 then it can be divided by 5,
if it ends in a multiple of 2 , then number is divisible by 2
if the digits added up are divisible by 3 then number is divisible by 3
that's how you choose, you first try to see if there is any number that can be a factor for all the numbers , if not then try 2,3,5 etc you gotto know the tables
40000
To find the least common multiple (LCM) for the given numbers, there are several methods you can use. The two most commonly used methods are the prime factorization method and the list method.
1. Prime Factorization Method:
- Start by finding the prime factorization of each number: 135 = 3^3 * 5, 56 = 2^3 * 7, and 150 = 2 * 3 * 5^2.
- Take all the prime factors from the three numbers, and include each to its highest power: 2^3 * 3^3 * 5^2 * 7.
- Multiply all these prime factors together: LCM = 2^3 * 3^3 * 5^2 * 7 = 8 * 27 * 25 * 7 = 37,800.
2. List Method:
- Start by listing the multiples of each number until you find a common multiple:
Multiples of 135: 135, 270, 405, 540, 675, 810, 945, ...
Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, ...
Multiples of 150: 150, 300, 450, 600, 750, 900, ...
- From the lists, we can see that 1,200 is the smallest common multiple for all three numbers.
- Therefore, LCM = 1,200.
Both methods will give you the correct answer. However, the prime factorization method is generally more efficient and allows you to find the LCM quickly, especially when dealing with larger numbers or more numbers.