Least Common Multiple (LCM) of 108 and 196
The least common multiple (LCM) of 108 and 196 is 5292.
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 108 and 196?
First, calculate the GCD of 108 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 196 = 0 remainder 108 |
| 2 | 196 ÷ 108 = 1 remainder 88 |
| 3 | 108 ÷ 88 = 1 remainder 20 |
| 4 | 88 ÷ 20 = 4 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 51 | 459 |
| 27 and 141 | 1269 |
| 175 and 67 | 11725 |
| 10 and 116 | 580 |
| 179 and 154 | 27566 |