Least Common Multiple (LCM) of 196 and 108
The least common multiple (LCM) of 196 and 108 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 196 and 108?
First, calculate the GCD of 196 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 108 = 1 remainder 88 |
| 2 | 108 ÷ 88 = 1 remainder 20 |
| 3 | 88 ÷ 20 = 4 remainder 8 |
| 4 | 20 ÷ 8 = 2 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 85 | 14535 |
| 175 and 78 | 13650 |
| 195 and 10 | 390 |
| 113 and 10 | 1130 |
| 10 and 120 | 120 |