Least Common Multiple (LCM) of 101 and 109
The least common multiple (LCM) of 101 and 109 is 11009.
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 109?
First, calculate the GCD of 101 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 109 = 0 remainder 101 |
| 2 | 109 ÷ 101 = 1 remainder 8 |
| 3 | 101 ÷ 8 = 12 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 12 | 2244 |
| 113 and 89 | 10057 |
| 143 and 63 | 9009 |
| 43 and 31 | 1333 |
| 106 and 198 | 10494 |