Least Common Multiple (LCM) of 69 and 170
The least common multiple (LCM) of 69 and 170 is 11730.
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 69 and 170?
First, calculate the GCD of 69 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 170 = 0 remainder 69 |
| 2 | 170 ÷ 69 = 2 remainder 32 |
| 3 | 69 ÷ 32 = 2 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 132 | 132 |
| 105 and 84 | 420 |
| 26 and 49 | 1274 |
| 136 and 13 | 1768 |
| 11 and 45 | 495 |