Least Common Multiple (LCM) of 126 and 161
The least common multiple (LCM) of 126 and 161 is 2898.
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 126 and 161?
First, calculate the GCD of 126 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 161 = 0 remainder 126 |
| 2 | 161 ÷ 126 = 1 remainder 35 |
| 3 | 126 ÷ 35 = 3 remainder 21 |
| 4 | 35 ÷ 21 = 1 remainder 14 |
| 5 | 21 ÷ 14 = 1 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 20 | 560 |
| 105 and 102 | 3570 |
| 110 and 165 | 330 |
| 165 and 100 | 3300 |
| 121 and 78 | 9438 |