Least Common Multiple (LCM) of 196 and 141
The least common multiple (LCM) of 196 and 141 is 27636.
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 141?
First, calculate the GCD of 196 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 141 = 1 remainder 55 |
| 2 | 141 ÷ 55 = 2 remainder 31 |
| 3 | 55 ÷ 31 = 1 remainder 24 |
| 4 | 31 ÷ 24 = 1 remainder 7 |
| 5 | 24 ÷ 7 = 3 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 115 | 805 |
| 71 and 48 | 3408 |
| 66 and 24 | 264 |
| 129 and 186 | 7998 |
| 169 and 189 | 31941 |