Least Common Multiple (LCM) of 196 and 114
The least common multiple (LCM) of 196 and 114 is 11172.
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 114?
First, calculate the GCD of 196 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 114 = 1 remainder 82 |
| 2 | 114 ÷ 82 = 1 remainder 32 |
| 3 | 82 ÷ 32 = 2 remainder 18 |
| 4 | 32 ÷ 18 = 1 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 107 | 8560 |
| 159 and 79 | 12561 |
| 32 and 29 | 928 |
| 176 and 102 | 8976 |
| 71 and 191 | 13561 |