Least Common Multiple (LCM) of 169 and 178
The least common multiple (LCM) of 169 and 178 is 30082.
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 178?
First, calculate the GCD of 169 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 178 = 0 remainder 169 |
| 2 | 178 ÷ 169 = 1 remainder 9 |
| 3 | 169 ÷ 9 = 18 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 191 | 5539 |
| 12 and 108 | 108 |
| 116 and 57 | 6612 |
| 58 and 200 | 5800 |
| 36 and 193 | 6948 |