Least Common Multiple (LCM) of 106 and 156
The least common multiple (LCM) of 106 and 156 is 8268.
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 156?
First, calculate the GCD of 106 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 156 = 0 remainder 106 |
| 2 | 156 ÷ 106 = 1 remainder 50 |
| 3 | 106 ÷ 50 = 2 remainder 6 |
| 4 | 50 ÷ 6 = 8 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 50 | 2150 |
| 71 and 188 | 13348 |
| 185 and 148 | 740 |
| 78 and 144 | 1872 |
| 191 and 35 | 6685 |