Least Common Multiple (LCM) of 118 and 196
The least common multiple (LCM) of 118 and 196 is 11564.
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 118 and 196?
First, calculate the GCD of 118 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 196 = 0 remainder 118 |
| 2 | 196 ÷ 118 = 1 remainder 78 |
| 3 | 118 ÷ 78 = 1 remainder 40 |
| 4 | 78 ÷ 40 = 1 remainder 38 |
| 5 | 40 ÷ 38 = 1 remainder 2 |
| 6 | 38 ÷ 2 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 44 | 836 |
| 55 and 200 | 2200 |
| 96 and 126 | 2016 |
| 12 and 171 | 684 |
| 125 and 133 | 16625 |