Least Common Multiple (LCM) of 155 and 178
The least common multiple (LCM) of 155 and 178 is 27590.
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 155 and 178?
First, calculate the GCD of 155 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 178 = 0 remainder 155 |
| 2 | 178 ÷ 155 = 1 remainder 23 |
| 3 | 155 ÷ 23 = 6 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 79 | 3002 |
| 100 and 22 | 1100 |
| 77 and 165 | 1155 |
| 68 and 151 | 10268 |
| 186 and 45 | 2790 |