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 |
|---|---|
| 31 and 134 | 4154 |
| 126 and 179 | 22554 |
| 189 and 165 | 10395 |
| 113 and 159 | 17967 |
| 59 and 79 | 4661 |