Least Common Multiple (LCM) of 106 and 132
The least common multiple (LCM) of 106 and 132 is 6996.
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 106 and 132?
First, calculate the GCD of 106 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 132 = 0 remainder 106 |
| 2 | 132 ÷ 106 = 1 remainder 26 |
| 3 | 106 ÷ 26 = 4 remainder 2 |
| 4 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 74 | 2220 |
| 115 and 81 | 9315 |
| 51 and 197 | 10047 |
| 53 and 165 | 8745 |
| 175 and 150 | 1050 |