Least Common Multiple (LCM) of 106 and 178
The least common multiple (LCM) of 106 and 178 is 9434.
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 106 and 178?
First, calculate the GCD of 106 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 178 = 0 remainder 106 |
| 2 | 178 ÷ 106 = 1 remainder 72 |
| 3 | 106 ÷ 72 = 1 remainder 34 |
| 4 | 72 ÷ 34 = 2 remainder 4 |
| 5 | 34 ÷ 4 = 8 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 82 | 1558 |
| 112 and 122 | 6832 |
| 144 and 58 | 4176 |
| 165 and 117 | 6435 |
| 113 and 48 | 5424 |