Least Common Multiple (LCM) of 106 and 167
The least common multiple (LCM) of 106 and 167 is 17702.
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 167?
First, calculate the GCD of 106 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 167 = 0 remainder 106 |
| 2 | 167 ÷ 106 = 1 remainder 61 |
| 3 | 106 ÷ 61 = 1 remainder 45 |
| 4 | 61 ÷ 45 = 1 remainder 16 |
| 5 | 45 ÷ 16 = 2 remainder 13 |
| 6 | 16 ÷ 13 = 1 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 11 | 22 |
| 46 and 67 | 3082 |
| 86 and 39 | 3354 |
| 93 and 30 | 930 |
| 114 and 85 | 9690 |