Least Common Multiple (LCM) of 104 and 150
The least common multiple (LCM) of 104 and 150 is 7800.
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 104 and 150?
First, calculate the GCD of 104 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 150 = 0 remainder 104 |
| 2 | 150 ÷ 104 = 1 remainder 46 |
| 3 | 104 ÷ 46 = 2 remainder 12 |
| 4 | 46 ÷ 12 = 3 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 12 | 180 |
| 22 and 150 | 1650 |
| 109 and 15 | 1635 |
| 112 and 33 | 3696 |
| 49 and 154 | 1078 |