Least Common Multiple (LCM) of 167 and 109
The least common multiple (LCM) of 167 and 109 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 167 and 109?
First, calculate the GCD of 167 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 109 = 1 remainder 58 |
| 2 | 109 ÷ 58 = 1 remainder 51 |
| 3 | 58 ÷ 51 = 1 remainder 7 |
| 4 | 51 ÷ 7 = 7 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 65 | 2080 |
| 154 and 189 | 4158 |
| 186 and 152 | 14136 |
| 110 and 36 | 1980 |
| 67 and 116 | 7772 |