Least Common Multiple (LCM) of 150 and 108
The least common multiple (LCM) of 150 and 108 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 150 and 108?
First, calculate the GCD of 150 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 108 = 1 remainder 42 |
| 2 | 108 ÷ 42 = 2 remainder 24 |
| 3 | 42 ÷ 24 = 1 remainder 18 |
| 4 | 24 ÷ 18 = 1 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 12 | 36 |
| 92 and 46 | 92 |
| 166 and 153 | 25398 |
| 10 and 120 | 120 |
| 160 and 42 | 3360 |