Least Common Multiple (LCM) of 150 and 104
The least common multiple (LCM) of 150 and 104 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 150 and 104?
First, calculate the GCD of 150 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 104 = 1 remainder 46 |
| 2 | 104 ÷ 46 = 2 remainder 12 |
| 3 | 46 ÷ 12 = 3 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 32 | 3488 |
| 57 and 114 | 114 |
| 115 and 40 | 920 |
| 17 and 31 | 527 |
| 116 and 198 | 11484 |