Least Common Multiple (LCM) of 169 and 115
The least common multiple (LCM) of 169 and 115 is 19435.
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 115?
First, calculate the GCD of 169 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 115 = 1 remainder 54 |
| 2 | 115 ÷ 54 = 2 remainder 7 |
| 3 | 54 ÷ 7 = 7 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 68 | 3400 |
| 120 and 37 | 4440 |
| 41 and 119 | 4879 |
| 78 and 144 | 1872 |
| 138 and 149 | 20562 |