Least Common Multiple (LCM) of 107 and 170
The least common multiple (LCM) of 107 and 170 is 18190.
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 107 and 170?
First, calculate the GCD of 107 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 170 = 0 remainder 107 |
| 2 | 170 ÷ 107 = 1 remainder 63 |
| 3 | 107 ÷ 63 = 1 remainder 44 |
| 4 | 63 ÷ 44 = 1 remainder 19 |
| 5 | 44 ÷ 19 = 2 remainder 6 |
| 6 | 19 ÷ 6 = 3 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 97 | 1358 |
| 119 and 43 | 5117 |
| 172 and 143 | 24596 |
| 95 and 20 | 380 |
| 39 and 42 | 546 |