Least Common Multiple (LCM) of 106 and 150
The least common multiple (LCM) of 106 and 150 is 7950.
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 150?
First, calculate the GCD of 106 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 150 = 0 remainder 106 |
| 2 | 150 ÷ 106 = 1 remainder 44 |
| 3 | 106 ÷ 44 = 2 remainder 18 |
| 4 | 44 ÷ 18 = 2 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 36 | 1980 |
| 60 and 121 | 7260 |
| 89 and 125 | 11125 |
| 124 and 15 | 1860 |
| 34 and 167 | 5678 |