Least Common Multiple (LCM) of 178 and 154
The least common multiple (LCM) of 178 and 154 is 13706.
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 154?
First, calculate the GCD of 178 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 154 = 1 remainder 24 |
| 2 | 154 ÷ 24 = 6 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 32 | 224 |
| 23 and 15 | 345 |
| 137 and 187 | 25619 |
| 147 and 137 | 20139 |
| 126 and 78 | 1638 |