Least Common Multiple (LCM) of 105 and 148
The least common multiple (LCM) of 105 and 148 is 15540.
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 105 and 148?
First, calculate the GCD of 105 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 148 = 0 remainder 105 |
| 2 | 148 ÷ 105 = 1 remainder 43 |
| 3 | 105 ÷ 43 = 2 remainder 19 |
| 4 | 43 ÷ 19 = 2 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 199 | 13333 |
| 32 and 85 | 2720 |
| 16 and 21 | 336 |
| 179 and 53 | 9487 |
| 110 and 131 | 14410 |