Least Common Multiple (LCM) of 196 and 101
The least common multiple (LCM) of 196 and 101 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 196 and 101?
First, calculate the GCD of 196 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 101 = 1 remainder 95 |
| 2 | 101 ÷ 95 = 1 remainder 6 |
| 3 | 95 ÷ 6 = 15 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 137 | 7535 |
| 149 and 10 | 1490 |
| 47 and 165 | 7755 |
| 45 and 23 | 1035 |
| 191 and 32 | 6112 |