Least Common Multiple (LCM) of 101 and 196
The least common multiple (LCM) of 101 and 196 is 19796.
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 101 and 196?
First, calculate the GCD of 101 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 196 = 0 remainder 101 |
| 2 | 196 ÷ 101 = 1 remainder 95 |
| 3 | 101 ÷ 95 = 1 remainder 6 |
| 4 | 95 ÷ 6 = 15 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 29 | 3393 |
| 199 and 194 | 38606 |
| 192 and 52 | 2496 |
| 92 and 145 | 13340 |
| 170 and 192 | 16320 |