Least Common Multiple (LCM) of 115 and 132
The least common multiple (LCM) of 115 and 132 is 15180.
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 115 and 132?
First, calculate the GCD of 115 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 132 = 0 remainder 115 |
| 2 | 132 ÷ 115 = 1 remainder 17 |
| 3 | 115 ÷ 17 = 6 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 114 | 4218 |
| 63 and 99 | 693 |
| 72 and 159 | 3816 |
| 104 and 107 | 11128 |
| 16 and 107 | 1712 |