Least Common Multiple (LCM) of 178 and 115
The least common multiple (LCM) of 178 and 115 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 178 and 115?
First, calculate the GCD of 178 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 115 = 1 remainder 63 |
| 2 | 115 ÷ 63 = 1 remainder 52 |
| 3 | 63 ÷ 52 = 1 remainder 11 |
| 4 | 52 ÷ 11 = 4 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 18 | 3330 |
| 72 and 132 | 792 |
| 24 and 19 | 456 |
| 89 and 75 | 6675 |
| 13 and 57 | 741 |