Least Common Multiple (LCM) of 132 and 37
The least common multiple (LCM) of 132 and 37 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 132 and 37?
First, calculate the GCD of 132 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 37 = 3 remainder 21 |
| 2 | 37 ÷ 21 = 1 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 160 | 1120 |
| 86 and 99 | 8514 |
| 112 and 72 | 1008 |
| 129 and 129 | 129 |
| 77 and 171 | 13167 |