Least Common Multiple (LCM) of 108 and 150
The least common multiple (LCM) of 108 and 150 is 2700.
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 108 and 150?
First, calculate the GCD of 108 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 150 = 0 remainder 108 |
| 2 | 150 ÷ 108 = 1 remainder 42 |
| 3 | 108 ÷ 42 = 2 remainder 24 |
| 4 | 42 ÷ 24 = 1 remainder 18 |
| 5 | 24 ÷ 18 = 1 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 162 | 2754 |
| 21 and 38 | 798 |
| 135 and 51 | 2295 |
| 13 and 77 | 1001 |
| 78 and 95 | 7410 |