Least Common Multiple (LCM) of 133 and 167
The least common multiple (LCM) of 133 and 167 is 22211.
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 133 and 167?
First, calculate the GCD of 133 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 167 = 0 remainder 133 |
| 2 | 167 ÷ 133 = 1 remainder 34 |
| 3 | 133 ÷ 34 = 3 remainder 31 |
| 4 | 34 ÷ 31 = 1 remainder 3 |
| 5 | 31 ÷ 3 = 10 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 37 | 2627 |
| 21 and 191 | 4011 |
| 12 and 155 | 1860 |
| 162 and 33 | 1782 |
| 86 and 148 | 6364 |