Least Common Multiple (LCM) of 106 and 147
The least common multiple (LCM) of 106 and 147 is 15582.
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 147?
First, calculate the GCD of 106 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 147 = 0 remainder 106 |
| 2 | 147 ÷ 106 = 1 remainder 41 |
| 3 | 106 ÷ 41 = 2 remainder 24 |
| 4 | 41 ÷ 24 = 1 remainder 17 |
| 5 | 24 ÷ 17 = 1 remainder 7 |
| 6 | 17 ÷ 7 = 2 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 106 | 9540 |
| 20 and 199 | 3980 |
| 92 and 189 | 17388 |
| 10 and 93 | 930 |
| 189 and 40 | 7560 |