Least Common Multiple (LCM) of 150 and 111
The least common multiple (LCM) of 150 and 111 is 5550.
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 111?
First, calculate the GCD of 150 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 111 = 1 remainder 39 |
| 2 | 111 ÷ 39 = 2 remainder 33 |
| 3 | 39 ÷ 33 = 1 remainder 6 |
| 4 | 33 ÷ 6 = 5 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 139 | 12510 |
| 159 and 130 | 20670 |
| 65 and 97 | 6305 |
| 35 and 138 | 4830 |
| 112 and 57 | 6384 |