Least Common Multiple (LCM) of 196 and 126
The least common multiple (LCM) of 196 and 126 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 196 and 126?
First, calculate the GCD of 196 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 126 = 1 remainder 70 |
| 2 | 126 ÷ 70 = 1 remainder 56 |
| 3 | 70 ÷ 56 = 1 remainder 14 |
| 4 | 56 ÷ 14 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 27 | 864 |
| 107 and 126 | 13482 |
| 115 and 30 | 690 |
| 88 and 126 | 5544 |
| 186 and 32 | 2976 |