Least Common Multiple (LCM) of 115 and 178
The least common multiple (LCM) of 115 and 178 is 20470.
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 178?
First, calculate the GCD of 115 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 178 = 0 remainder 115 |
| 2 | 178 ÷ 115 = 1 remainder 63 |
| 3 | 115 ÷ 63 = 1 remainder 52 |
| 4 | 63 ÷ 52 = 1 remainder 11 |
| 5 | 52 ÷ 11 = 4 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 96 | 8736 |
| 99 and 41 | 4059 |
| 84 and 29 | 2436 |
| 93 and 14 | 1302 |
| 158 and 178 | 14062 |