Least Common Multiple (LCM) of 150 and 67
The least common multiple (LCM) of 150 and 67 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 150 and 67?
First, calculate the GCD of 150 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 67 = 2 remainder 16 |
| 2 | 67 ÷ 16 = 4 remainder 3 |
| 3 | 16 ÷ 3 = 5 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 78 | 12714 |
| 179 and 129 | 23091 |
| 30 and 50 | 150 |
| 73 and 62 | 4526 |
| 178 and 25 | 4450 |