Least Common Multiple (LCM) of 132 and 188
The least common multiple (LCM) of 132 and 188 is 6204.
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 188?
First, calculate the GCD of 132 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 188 = 0 remainder 132 |
| 2 | 188 ÷ 132 = 1 remainder 56 |
| 3 | 132 ÷ 56 = 2 remainder 20 |
| 4 | 56 ÷ 20 = 2 remainder 16 |
| 5 | 20 ÷ 16 = 1 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 118 | 7670 |
| 42 and 58 | 1218 |
| 21 and 108 | 756 |
| 59 and 156 | 9204 |
| 48 and 120 | 240 |