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 |
|---|---|
| 197 and 196 | 38612 |
| 101 and 68 | 6868 |
| 101 and 174 | 17574 |
| 122 and 77 | 9394 |
| 95 and 64 | 6080 |