Least Common Multiple (LCM) of 18 and 167
The least common multiple (LCM) of 18 and 167 is 3006.
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 18 and 167?
First, calculate the GCD of 18 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 167 = 0 remainder 18 |
| 2 | 167 ÷ 18 = 9 remainder 5 |
| 3 | 18 ÷ 5 = 3 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 151 | 24462 |
| 192 and 98 | 9408 |
| 154 and 154 | 154 |
| 126 and 153 | 2142 |
| 186 and 129 | 7998 |