Least Common Multiple (LCM) of 123 and 178
The least common multiple (LCM) of 123 and 178 is 21894.
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 123 and 178?
First, calculate the GCD of 123 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 178 = 0 remainder 123 |
| 2 | 178 ÷ 123 = 1 remainder 55 |
| 3 | 123 ÷ 55 = 2 remainder 13 |
| 4 | 55 ÷ 13 = 4 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 176 | 2112 |
| 52 and 172 | 2236 |
| 147 and 168 | 1176 |
| 153 and 69 | 3519 |
| 164 and 165 | 27060 |