Least Common Multiple (LCM) of 106 and 170
The least common multiple (LCM) of 106 and 170 is 9010.
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 170?
First, calculate the GCD of 106 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 170 = 0 remainder 106 |
| 2 | 170 ÷ 106 = 1 remainder 64 |
| 3 | 106 ÷ 64 = 1 remainder 42 |
| 4 | 64 ÷ 42 = 1 remainder 22 |
| 5 | 42 ÷ 22 = 1 remainder 20 |
| 6 | 22 ÷ 20 = 1 remainder 2 |
| 7 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 75 | 12450 |
| 164 and 138 | 11316 |
| 71 and 131 | 9301 |
| 49 and 163 | 7987 |
| 40 and 176 | 880 |