Least Common Multiple (LCM) of 108 and 167
The least common multiple (LCM) of 108 and 167 is 18036.
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 108 and 167?
First, calculate the GCD of 108 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 167 = 0 remainder 108 |
| 2 | 167 ÷ 108 = 1 remainder 59 |
| 3 | 108 ÷ 59 = 1 remainder 49 |
| 4 | 59 ÷ 49 = 1 remainder 10 |
| 5 | 49 ÷ 10 = 4 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 188 | 2444 |
| 13 and 112 | 1456 |
| 164 and 49 | 8036 |
| 179 and 59 | 10561 |
| 99 and 19 | 1881 |