Least Common Multiple (LCM) of 12 and 167
The least common multiple (LCM) of 12 and 167 is 2004.
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 12 and 167?
First, calculate the GCD of 12 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 167 = 0 remainder 12 |
| 2 | 167 ÷ 12 = 13 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 106 | 10494 |
| 133 and 50 | 6650 |
| 61 and 120 | 7320 |
| 198 and 199 | 39402 |
| 20 and 68 | 340 |