Least Common Multiple (LCM) of 169 and 107
The least common multiple (LCM) of 169 and 107 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 169 and 107?
First, calculate the GCD of 169 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 107 = 1 remainder 62 |
| 2 | 107 ÷ 62 = 1 remainder 45 |
| 3 | 62 ÷ 45 = 1 remainder 17 |
| 4 | 45 ÷ 17 = 2 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 179 | 22912 |
| 160 and 24 | 480 |
| 16 and 56 | 112 |
| 32 and 172 | 1376 |
| 198 and 167 | 33066 |