Least Common Multiple (LCM) of 132 and 167
The least common multiple (LCM) of 132 and 167 is 22044.
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 132 and 167?
First, calculate the GCD of 132 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 167 = 0 remainder 132 |
| 2 | 167 ÷ 132 = 1 remainder 35 |
| 3 | 132 ÷ 35 = 3 remainder 27 |
| 4 | 35 ÷ 27 = 1 remainder 8 |
| 5 | 27 ÷ 8 = 3 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 142 | 22294 |
| 172 and 104 | 4472 |
| 17 and 136 | 136 |
| 151 and 91 | 13741 |
| 109 and 80 | 8720 |