Least Common Multiple (LCM) of 107 and 169
The least common multiple (LCM) of 107 and 169 is 18083.
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 169?
First, calculate the GCD of 107 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 169 = 0 remainder 107 |
| 2 | 169 ÷ 107 = 1 remainder 62 |
| 3 | 107 ÷ 62 = 1 remainder 45 |
| 4 | 62 ÷ 45 = 1 remainder 17 |
| 5 | 45 ÷ 17 = 2 remainder 11 |
| 6 | 17 ÷ 11 = 1 remainder 6 |
| 7 | 11 ÷ 6 = 1 remainder 5 |
| 8 | 6 ÷ 5 = 1 remainder 1 |
| 9 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 12 | 1524 |
| 53 and 157 | 8321 |
| 34 and 36 | 612 |
| 137 and 140 | 19180 |
| 198 and 82 | 8118 |