Least Common Multiple (LCM) of 105 and 132
The least common multiple (LCM) of 105 and 132 is 4620.
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 105 and 132?
First, calculate the GCD of 105 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 132 = 0 remainder 105 |
| 2 | 132 ÷ 105 = 1 remainder 27 |
| 3 | 105 ÷ 27 = 3 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 132 | 6600 |
| 55 and 68 | 3740 |
| 22 and 109 | 2398 |
| 84 and 108 | 756 |
| 64 and 113 | 7232 |