Least Common Multiple (LCM) of 67 and 106
The least common multiple (LCM) of 67 and 106 is 7102.
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 67 and 106?
First, calculate the GCD of 67 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 106 = 0 remainder 67 |
| 2 | 106 ÷ 67 = 1 remainder 39 |
| 3 | 67 ÷ 39 = 1 remainder 28 |
| 4 | 39 ÷ 28 = 1 remainder 11 |
| 5 | 28 ÷ 11 = 2 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 20 | 1060 |
| 10 and 13 | 130 |
| 175 and 181 | 31675 |
| 77 and 65 | 5005 |
| 147 and 49 | 147 |