Least Common Multiple (LCM) of 106 and 172
The least common multiple (LCM) of 106 and 172 is 9116.
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 172?
First, calculate the GCD of 106 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 172 = 0 remainder 106 |
| 2 | 172 ÷ 106 = 1 remainder 66 |
| 3 | 106 ÷ 66 = 1 remainder 40 |
| 4 | 66 ÷ 40 = 1 remainder 26 |
| 5 | 40 ÷ 26 = 1 remainder 14 |
| 6 | 26 ÷ 14 = 1 remainder 12 |
| 7 | 14 ÷ 12 = 1 remainder 2 |
| 8 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 156 | 10452 |
| 106 and 23 | 2438 |
| 59 and 29 | 1711 |
| 108 and 56 | 1512 |
| 73 and 125 | 9125 |