Least Common Multiple (LCM) of 132 and 200
The least common multiple (LCM) of 132 and 200 is 6600.
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 200?
First, calculate the GCD of 132 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 200 = 0 remainder 132 |
| 2 | 200 ÷ 132 = 1 remainder 68 |
| 3 | 132 ÷ 68 = 1 remainder 64 |
| 4 | 68 ÷ 64 = 1 remainder 4 |
| 5 | 64 ÷ 4 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 192 | 4032 |
| 49 and 59 | 2891 |
| 54 and 39 | 702 |
| 37 and 65 | 2405 |
| 125 and 97 | 12125 |