Least Common Multiple (LCM) of 89 and 155
The least common multiple (LCM) of 89 and 155 is 13795.
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 89 and 155?
First, calculate the GCD of 89 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 155 = 0 remainder 89 |
| 2 | 155 ÷ 89 = 1 remainder 66 |
| 3 | 89 ÷ 66 = 1 remainder 23 |
| 4 | 66 ÷ 23 = 2 remainder 20 |
| 5 | 23 ÷ 20 = 1 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 182 | 15470 |
| 99 and 41 | 4059 |
| 138 and 177 | 8142 |
| 173 and 88 | 15224 |
| 183 and 55 | 10065 |