Least Common Multiple (LCM) of 196 and 155
The least common multiple (LCM) of 196 and 155 is 30380.
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 155?
First, calculate the GCD of 196 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 155 = 1 remainder 41 |
| 2 | 155 ÷ 41 = 3 remainder 32 |
| 3 | 41 ÷ 32 = 1 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 142 | 5680 |
| 47 and 37 | 1739 |
| 78 and 71 | 5538 |
| 163 and 188 | 30644 |
| 116 and 64 | 1856 |