Least Common Multiple (LCM) of 123 and 196
The least common multiple (LCM) of 123 and 196 is 24108.
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 123 and 196?
First, calculate the GCD of 123 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 196 = 0 remainder 123 |
| 2 | 196 ÷ 123 = 1 remainder 73 |
| 3 | 123 ÷ 73 = 1 remainder 50 |
| 4 | 73 ÷ 50 = 1 remainder 23 |
| 5 | 50 ÷ 23 = 2 remainder 4 |
| 6 | 23 ÷ 4 = 5 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 20 | 660 |
| 40 and 198 | 3960 |
| 180 and 28 | 1260 |
| 139 and 144 | 20016 |
| 34 and 28 | 476 |