Least Common Multiple (LCM) of 39 and 132
The least common multiple (LCM) of 39 and 132 is 1716.
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 39 and 132?
First, calculate the GCD of 39 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 132 = 0 remainder 39 |
| 2 | 132 ÷ 39 = 3 remainder 15 |
| 3 | 39 ÷ 15 = 2 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 30 | 30 |
| 32 and 192 | 192 |
| 50 and 152 | 3800 |
| 161 and 77 | 1771 |
| 162 and 189 | 1134 |