Least Common Multiple (LCM) of 37 and 132
The least common multiple (LCM) of 37 and 132 is 4884.
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 37 and 132?
First, calculate the GCD of 37 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 132 = 0 remainder 37 |
| 2 | 132 ÷ 37 = 3 remainder 21 |
| 3 | 37 ÷ 21 = 1 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 13 | 1664 |
| 177 and 45 | 2655 |
| 78 and 100 | 3900 |
| 17 and 172 | 2924 |
| 198 and 176 | 1584 |