Least Common Multiple (LCM) of 155 and 109
The least common multiple (LCM) of 155 and 109 is 16895.
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 155 and 109?
First, calculate the GCD of 155 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 109 = 1 remainder 46 |
| 2 | 109 ÷ 46 = 2 remainder 17 |
| 3 | 46 ÷ 17 = 2 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 118 | 15930 |
| 196 and 12 | 588 |
| 121 and 46 | 5566 |
| 99 and 173 | 17127 |
| 14 and 71 | 994 |