Least Common Multiple (LCM) of 137 and 150
The least common multiple (LCM) of 137 and 150 is 20550.
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 137 and 150?
First, calculate the GCD of 137 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 150 = 0 remainder 137 |
| 2 | 150 ÷ 137 = 1 remainder 13 |
| 3 | 137 ÷ 13 = 10 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 20 | 580 |
| 166 and 179 | 29714 |
| 67 and 76 | 5092 |
| 14 and 28 | 28 |
| 108 and 123 | 4428 |