Least Common Multiple (LCM) of 114 and 178
The least common multiple (LCM) of 114 and 178 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 114 and 178?
First, calculate the GCD of 114 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 178 = 0 remainder 114 |
| 2 | 178 ÷ 114 = 1 remainder 64 |
| 3 | 114 ÷ 64 = 1 remainder 50 |
| 4 | 64 ÷ 50 = 1 remainder 14 |
| 5 | 50 ÷ 14 = 3 remainder 8 |
| 6 | 14 ÷ 8 = 1 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 133 | 13566 |
| 178 and 167 | 29726 |
| 163 and 16 | 2608 |
| 21 and 16 | 336 |
| 195 and 165 | 2145 |