Least Common Multiple (LCM) of 99 and 167
The least common multiple (LCM) of 99 and 167 is 16533.
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 99 and 167?
First, calculate the GCD of 99 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 167 = 0 remainder 99 |
| 2 | 167 ÷ 99 = 1 remainder 68 |
| 3 | 99 ÷ 68 = 1 remainder 31 |
| 4 | 68 ÷ 31 = 2 remainder 6 |
| 5 | 31 ÷ 6 = 5 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 30 | 1170 |
| 129 and 57 | 2451 |
| 42 and 147 | 294 |
| 174 and 124 | 10788 |
| 28 and 184 | 1288 |