Least Common Multiple (LCM) of 106 and 60
The least common multiple (LCM) of 106 and 60 is 3180.
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 60?
First, calculate the GCD of 106 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 60 = 1 remainder 46 |
| 2 | 60 ÷ 46 = 1 remainder 14 |
| 3 | 46 ÷ 14 = 3 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 86 | 8170 |
| 46 and 17 | 782 |
| 192 and 156 | 2496 |
| 18 and 45 | 90 |
| 146 and 149 | 21754 |