Least Common Multiple (LCM) of 196 and 58
The least common multiple (LCM) of 196 and 58 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 196 and 58?
First, calculate the GCD of 196 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 58 = 3 remainder 22 |
| 2 | 58 ÷ 22 = 2 remainder 14 |
| 3 | 22 ÷ 14 = 1 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 113 | 10170 |
| 48 and 130 | 3120 |
| 141 and 68 | 9588 |
| 17 and 162 | 2754 |
| 153 and 136 | 1224 |