Least Common Multiple (LCM) of 26 and 150
The least common multiple (LCM) of 26 and 150 is 1950.
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 26 and 150?
First, calculate the GCD of 26 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 150 = 0 remainder 26 |
| 2 | 150 ÷ 26 = 5 remainder 20 |
| 3 | 26 ÷ 20 = 1 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 107 | 17548 |
| 145 and 120 | 3480 |
| 22 and 45 | 990 |
| 149 and 74 | 11026 |
| 147 and 59 | 8673 |