Least Common Multiple (LCM) of 58 and 196
The least common multiple (LCM) of 58 and 196 is 5684.
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 58 and 196?
First, calculate the GCD of 58 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 196 = 0 remainder 58 |
| 2 | 196 ÷ 58 = 3 remainder 22 |
| 3 | 58 ÷ 22 = 2 remainder 14 |
| 4 | 22 ÷ 14 = 1 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 48 | 144 |
| 39 and 134 | 5226 |
| 167 and 95 | 15865 |
| 120 and 155 | 3720 |
| 17 and 126 | 2142 |