Least Common Multiple (LCM) of 57 and 196
The least common multiple (LCM) of 57 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 57 and 196?
First, calculate the GCD of 57 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 196 = 0 remainder 57 |
| 2 | 196 ÷ 57 = 3 remainder 25 |
| 3 | 57 ÷ 25 = 2 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 188 | 9400 |
| 139 and 186 | 25854 |
| 34 and 84 | 1428 |
| 84 and 134 | 5628 |
| 111 and 53 | 5883 |