Least Common Multiple (LCM) of 196 and 118
The least common multiple (LCM) of 196 and 118 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 196 and 118?
First, calculate the GCD of 196 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 118 = 1 remainder 78 |
| 2 | 118 ÷ 78 = 1 remainder 40 |
| 3 | 78 ÷ 40 = 1 remainder 38 |
| 4 | 40 ÷ 38 = 1 remainder 2 |
| 5 | 38 ÷ 2 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 69 | 6762 |
| 79 and 138 | 10902 |
| 61 and 101 | 6161 |
| 102 and 74 | 3774 |
| 158 and 100 | 7900 |