Least Common Multiple (LCM) of 118 and 167
The least common multiple (LCM) of 118 and 167 is 19706.
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 118 and 167?
First, calculate the GCD of 118 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 167 = 0 remainder 118 |
| 2 | 167 ÷ 118 = 1 remainder 49 |
| 3 | 118 ÷ 49 = 2 remainder 20 |
| 4 | 49 ÷ 20 = 2 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 144 | 3024 |
| 59 and 174 | 10266 |
| 69 and 29 | 2001 |
| 151 and 39 | 5889 |
| 169 and 14 | 2366 |