Least Common Multiple (LCM) of 115 and 169
The least common multiple (LCM) of 115 and 169 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 115 and 169?
First, calculate the GCD of 115 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 169 = 0 remainder 115 |
| 2 | 169 ÷ 115 = 1 remainder 54 |
| 3 | 115 ÷ 54 = 2 remainder 7 |
| 4 | 54 ÷ 7 = 7 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 178 | 12282 |
| 200 and 170 | 3400 |
| 57 and 114 | 114 |
| 138 and 29 | 4002 |
| 122 and 107 | 13054 |