Least Common Multiple (LCM) of 114 and 155
The least common multiple (LCM) of 114 and 155 is 17670.
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 114 and 155?
First, calculate the GCD of 114 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 155 = 0 remainder 114 |
| 2 | 155 ÷ 114 = 1 remainder 41 |
| 3 | 114 ÷ 41 = 2 remainder 32 |
| 4 | 41 ÷ 32 = 1 remainder 9 |
| 5 | 32 ÷ 9 = 3 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 14 | 154 |
| 32 and 163 | 5216 |
| 99 and 31 | 3069 |
| 177 and 198 | 11682 |
| 145 and 145 | 145 |