Least Common Multiple (LCM) of 196 and 113
The least common multiple (LCM) of 196 and 113 is 22148.
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 113?
First, calculate the GCD of 196 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 113 = 1 remainder 83 |
| 2 | 113 ÷ 83 = 1 remainder 30 |
| 3 | 83 ÷ 30 = 2 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 82 | 1066 |
| 21 and 40 | 840 |
| 53 and 187 | 9911 |
| 145 and 36 | 5220 |
| 68 and 146 | 4964 |