Least Common Multiple (LCM) of 114 and 196
The least common multiple (LCM) of 114 and 196 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 114 and 196?
First, calculate the GCD of 114 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 196 = 0 remainder 114 |
| 2 | 196 ÷ 114 = 1 remainder 82 |
| 3 | 114 ÷ 82 = 1 remainder 32 |
| 4 | 82 ÷ 32 = 2 remainder 18 |
| 5 | 32 ÷ 18 = 1 remainder 14 |
| 6 | 18 ÷ 14 = 1 remainder 4 |
| 7 | 14 ÷ 4 = 3 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 29 | 5249 |
| 149 and 158 | 23542 |
| 90 and 53 | 4770 |
| 79 and 53 | 4187 |
| 53 and 93 | 4929 |