Least Common Multiple (LCM) of 178 and 114
The least common multiple (LCM) of 178 and 114 is 10146.
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 114?
First, calculate the GCD of 178 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 114 = 1 remainder 64 |
| 2 | 114 ÷ 64 = 1 remainder 50 |
| 3 | 64 ÷ 50 = 1 remainder 14 |
| 4 | 50 ÷ 14 = 3 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 14 | 1974 |
| 82 and 31 | 2542 |
| 175 and 149 | 26075 |
| 128 and 172 | 5504 |
| 200 and 196 | 9800 |