Least Common Multiple (LCM) of 109 and 167
The least common multiple (LCM) of 109 and 167 is 18203.
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 109 and 167?
First, calculate the GCD of 109 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 167 = 0 remainder 109 |
| 2 | 167 ÷ 109 = 1 remainder 58 |
| 3 | 109 ÷ 58 = 1 remainder 51 |
| 4 | 58 ÷ 51 = 1 remainder 7 |
| 5 | 51 ÷ 7 = 7 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 179 | 19690 |
| 53 and 132 | 6996 |
| 37 and 56 | 2072 |
| 200 and 109 | 21800 |
| 46 and 183 | 8418 |