Least Common Multiple (LCM) of 106 and 67
The least common multiple (LCM) of 106 and 67 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 106 and 67?
First, calculate the GCD of 106 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 67 = 1 remainder 39 |
| 2 | 67 ÷ 39 = 1 remainder 28 |
| 3 | 39 ÷ 28 = 1 remainder 11 |
| 4 | 28 ÷ 11 = 2 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 108 | 1080 |
| 171 and 161 | 27531 |
| 54 and 17 | 918 |
| 62 and 180 | 5580 |
| 55 and 28 | 1540 |