Least Common Multiple (LCM) of 83 and 150
The least common multiple (LCM) of 83 and 150 is 12450.
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 83 and 150?
First, calculate the GCD of 83 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 150 = 0 remainder 83 |
| 2 | 150 ÷ 83 = 1 remainder 67 |
| 3 | 83 ÷ 67 = 1 remainder 16 |
| 4 | 67 ÷ 16 = 4 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 112 | 1008 |
| 27 and 45 | 135 |
| 36 and 69 | 828 |
| 136 and 31 | 4216 |
| 61 and 69 | 4209 |