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 |
|---|---|
| 175 and 131 | 22925 |
| 109 and 112 | 12208 |
| 43 and 101 | 4343 |
| 152 and 137 | 20824 |
| 14 and 41 | 574 |