Final answer:
To find the LCM of 40 and 90 using the ladder division method, divide them by common prime factors until you can't divide anymore, then multiply all the prime factors obtained to get the LCM, which in this case is 360.
Step-by-step explanation:
To find the Least Common Multiple (LCM) of 40 and 90 using the ladder division method, you need to follow these steps:
- Write the two numbers, 40 and 90, next to each other as they are the numbers we're finding the LCM for.
- Find a prime number that can evenly divide at least one of the numbers, such as 2.
- Divide each number by 2, which is the first prime number we've chosen. If 2 can't divide a number, just write down that number. After the division, you should have 20 and 45.
- Continue to find primes that can evenly divide the numbers you obtain. Next would be dividing them both by 5, giving you 4 and 9.
- Since 4 is 2 squared, divide it by 2 two times. This leads to two 2s written below the number 4, and the 9 remains unchanged.
- Now 9 is 3 squared, so divide it by 3 two times. Add the two 3s below the number 9.
- Multiply all the prime factors you wrote underneath the numbers to get the LCM. This gives you 2 * 2 * 2 * 5 * 3 * 3 = 360.
The LCM of the two numbers 40 and 90 is 360.