Least Common Multiple (LCM) of 178 and 126
The least common multiple (LCM) of 178 and 126 is 11214.
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 126?
First, calculate the GCD of 178 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 126 = 1 remainder 52 |
| 2 | 126 ÷ 52 = 2 remainder 22 |
| 3 | 52 ÷ 22 = 2 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 138 | 15042 |
| 120 and 185 | 4440 |
| 123 and 30 | 1230 |
| 64 and 75 | 4800 |
| 174 and 113 | 19662 |