Least Common Multiple (LCM) of 65 and 155
The least common multiple (LCM) of 65 and 155 is 2015.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 65 and 155?
First, calculate the GCD of 65 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 155 = 0 remainder 65 |
| 2 | 155 ÷ 65 = 2 remainder 25 |
| 3 | 65 ÷ 25 = 2 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 189 | 3024 |
| 128 and 35 | 4480 |
| 77 and 56 | 616 |
| 83 and 56 | 4648 |
| 15 and 190 | 570 |