Least Common Multiple (LCM) of 150 and 106
The least common multiple (LCM) of 150 and 106 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 150 and 106?
First, calculate the GCD of 150 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 106 = 1 remainder 44 |
| 2 | 106 ÷ 44 = 2 remainder 18 |
| 3 | 44 ÷ 18 = 2 remainder 8 |
| 4 | 18 ÷ 8 = 2 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 164 | 25420 |
| 65 and 27 | 1755 |
| 174 and 188 | 16356 |
| 11 and 187 | 187 |
| 170 and 14 | 1190 |