Least Common Multiple (LCM) of 115 and 154
The least common multiple (LCM) of 115 and 154 is 17710.
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 115 and 154?
First, calculate the GCD of 115 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 154 = 0 remainder 115 |
| 2 | 154 ÷ 115 = 1 remainder 39 |
| 3 | 115 ÷ 39 = 2 remainder 37 |
| 4 | 39 ÷ 37 = 1 remainder 2 |
| 5 | 37 ÷ 2 = 18 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 113 | 6441 |
| 54 and 47 | 2538 |
| 180 and 52 | 2340 |
| 76 and 63 | 4788 |
| 22 and 51 | 1122 |