Least Common Multiple (LCM) of 67 and 150
The least common multiple (LCM) of 67 and 150 is 10050.
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 67 and 150?
First, calculate the GCD of 67 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 150 = 0 remainder 67 |
| 2 | 150 ÷ 67 = 2 remainder 16 |
| 3 | 67 ÷ 16 = 4 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 169 | 16900 |
| 25 and 48 | 1200 |
| 180 and 154 | 13860 |
| 190 and 81 | 15390 |
| 119 and 46 | 5474 |