Least Common Multiple (LCM) of 55 and 150
The least common multiple (LCM) of 55 and 150 is 1650.
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 55 and 150?
First, calculate the GCD of 55 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 150 = 0 remainder 55 |
| 2 | 150 ÷ 55 = 2 remainder 40 |
| 3 | 55 ÷ 40 = 1 remainder 15 |
| 4 | 40 ÷ 15 = 2 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 154 | 11550 |
| 41 and 82 | 82 |
| 150 and 155 | 4650 |
| 178 and 95 | 16910 |
| 150 and 102 | 2550 |