Least Common Multiple (LCM) of 106 and 121
The least common multiple (LCM) of 106 and 121 is 12826.
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 106 and 121?
First, calculate the GCD of 106 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 121 = 0 remainder 106 |
| 2 | 121 ÷ 106 = 1 remainder 15 |
| 3 | 106 ÷ 15 = 7 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 85 | 2805 |
| 85 and 71 | 6035 |
| 105 and 80 | 1680 |
| 83 and 152 | 12616 |
| 53 and 132 | 6996 |