Least Common Multiple (LCM) of 167 and 108
The least common multiple (LCM) of 167 and 108 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 167 and 108?
First, calculate the GCD of 167 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 108 = 1 remainder 59 |
| 2 | 108 ÷ 59 = 1 remainder 49 |
| 3 | 59 ÷ 49 = 1 remainder 10 |
| 4 | 49 ÷ 10 = 4 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 137 | 17673 |
| 157 and 15 | 2355 |
| 142 and 15 | 2130 |
| 128 and 97 | 12416 |
| 19 and 113 | 2147 |