Least Common Multiple (LCM) of 126 and 196
The least common multiple (LCM) of 126 and 196 is 1764.
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 126 and 196?
First, calculate the GCD of 126 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 196 = 0 remainder 126 |
| 2 | 196 ÷ 126 = 1 remainder 70 |
| 3 | 126 ÷ 70 = 1 remainder 56 |
| 4 | 70 ÷ 56 = 1 remainder 14 |
| 5 | 56 ÷ 14 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 67 | 10251 |
| 20 and 61 | 1220 |
| 129 and 144 | 6192 |
| 71 and 199 | 14129 |
| 112 and 142 | 7952 |