Least Common Multiple (LCM) of 106 and 125
The least common multiple (LCM) of 106 and 125 is 13250.
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 125?
First, calculate the GCD of 106 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 125 = 0 remainder 106 |
| 2 | 125 ÷ 106 = 1 remainder 19 |
| 3 | 106 ÷ 19 = 5 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 71 | 3195 |
| 138 and 110 | 7590 |
| 80 and 146 | 5840 |
| 44 and 49 | 2156 |
| 44 and 112 | 1232 |