Least Common Multiple (LCM) of 132 and 193
The least common multiple (LCM) of 132 and 193 is 25476.
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 193?
First, calculate the GCD of 132 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 193 = 0 remainder 132 |
| 2 | 193 ÷ 132 = 1 remainder 61 |
| 3 | 132 ÷ 61 = 2 remainder 10 |
| 4 | 61 ÷ 10 = 6 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 99 | 3960 |
| 37 and 77 | 2849 |
| 162 and 168 | 4536 |
| 97 and 182 | 17654 |
| 176 and 59 | 10384 |