Least Common Multiple (LCM) of 106 and 174
The least common multiple (LCM) of 106 and 174 is 9222.
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 174?
First, calculate the GCD of 106 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 174 = 0 remainder 106 |
| 2 | 174 ÷ 106 = 1 remainder 68 |
| 3 | 106 ÷ 68 = 1 remainder 38 |
| 4 | 68 ÷ 38 = 1 remainder 30 |
| 5 | 38 ÷ 30 = 1 remainder 8 |
| 6 | 30 ÷ 8 = 3 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 194 | 12804 |
| 26 and 172 | 2236 |
| 157 and 94 | 14758 |
| 104 and 55 | 5720 |
| 193 and 105 | 20265 |