Least Common Multiple (LCM) of 31 and 132
The least common multiple (LCM) of 31 and 132 is 4092.
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 31 and 132?
First, calculate the GCD of 31 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 132 = 0 remainder 31 |
| 2 | 132 ÷ 31 = 4 remainder 8 |
| 3 | 31 ÷ 8 = 3 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 66 | 4422 |
| 113 and 54 | 6102 |
| 111 and 162 | 5994 |
| 21 and 125 | 2625 |
| 104 and 131 | 13624 |