Least Common Multiple (LCM) of 91 and 132
The least common multiple (LCM) of 91 and 132 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 91 and 132?
First, calculate the GCD of 91 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 132 = 0 remainder 91 |
| 2 | 132 ÷ 91 = 1 remainder 41 |
| 3 | 91 ÷ 41 = 2 remainder 9 |
| 4 | 41 ÷ 9 = 4 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 152 | 10184 |
| 12 and 105 | 420 |
| 193 and 136 | 26248 |
| 66 and 104 | 3432 |
| 165 and 120 | 1320 |