Least Common Multiple (LCM) of 60 and 106
The least common multiple (LCM) of 60 and 106 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 60 and 106?
First, calculate the GCD of 60 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 106 = 0 remainder 60 |
| 2 | 106 ÷ 60 = 1 remainder 46 |
| 3 | 60 ÷ 46 = 1 remainder 14 |
| 4 | 46 ÷ 14 = 3 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 180 | 180 |
| 153 and 58 | 8874 |
| 109 and 16 | 1744 |
| 53 and 94 | 4982 |
| 129 and 162 | 6966 |