Least Common Multiple (LCM) of 132 and 67
The least common multiple (LCM) of 132 and 67 is 8844.
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 67?
First, calculate the GCD of 132 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 67 = 1 remainder 65 |
| 2 | 67 ÷ 65 = 1 remainder 2 |
| 3 | 65 ÷ 2 = 32 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 96 | 16608 |
| 116 and 97 | 11252 |
| 112 and 175 | 2800 |
| 90 and 181 | 16290 |
| 90 and 171 | 1710 |