Least Common Multiple (LCM) of 109 and 178
The least common multiple (LCM) of 109 and 178 is 19402.
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 178?
First, calculate the GCD of 109 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 178 = 0 remainder 109 |
| 2 | 178 ÷ 109 = 1 remainder 69 |
| 3 | 109 ÷ 69 = 1 remainder 40 |
| 4 | 69 ÷ 40 = 1 remainder 29 |
| 5 | 40 ÷ 29 = 1 remainder 11 |
| 6 | 29 ÷ 11 = 2 remainder 7 |
| 7 | 11 ÷ 7 = 1 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 56 | 392 |
| 24 and 33 | 264 |
| 29 and 60 | 1740 |
| 150 and 78 | 1950 |
| 56 and 179 | 10024 |