Least Common Multiple (LCM) of 109 and 169
The least common multiple (LCM) of 109 and 169 is 18421.
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 109 and 169?
First, calculate the GCD of 109 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 169 = 0 remainder 109 |
| 2 | 169 ÷ 109 = 1 remainder 60 |
| 3 | 109 ÷ 60 = 1 remainder 49 |
| 4 | 60 ÷ 49 = 1 remainder 11 |
| 5 | 49 ÷ 11 = 4 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 103 | 1854 |
| 64 and 197 | 12608 |
| 35 and 142 | 4970 |
| 111 and 27 | 999 |
| 66 and 32 | 1056 |