Least Common Multiple (LCM) of 132 and 91
The least common multiple (LCM) of 132 and 91 is 12012.
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 91?
First, calculate the GCD of 132 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 91 = 1 remainder 41 |
| 2 | 91 ÷ 41 = 2 remainder 9 |
| 3 | 41 ÷ 9 = 4 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 45 | 1035 |
| 173 and 47 | 8131 |
| 113 and 126 | 14238 |
| 118 and 188 | 11092 |
| 82 and 104 | 4264 |