Least Common Multiple (LCM) of 117 and 154
The least common multiple (LCM) of 117 and 154 is 18018.
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 117 and 154?
First, calculate the GCD of 117 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 154 = 0 remainder 117 |
| 2 | 154 ÷ 117 = 1 remainder 37 |
| 3 | 117 ÷ 37 = 3 remainder 6 |
| 4 | 37 ÷ 6 = 6 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 180 | 540 |
| 29 and 194 | 5626 |
| 39 and 21 | 273 |
| 197 and 61 | 12017 |
| 109 and 200 | 21800 |