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 |
|---|---|
| 86 and 151 | 12986 |
| 194 and 136 | 13192 |
| 148 and 114 | 8436 |
| 179 and 91 | 16289 |
| 151 and 147 | 22197 |