Least Common Multiple (LCM) of 141 and 105
The least common multiple (LCM) of 141 and 105 is 4935.
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 141 and 105?
First, calculate the GCD of 141 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 141 ÷ 105 = 1 remainder 36 |
| 2 | 105 ÷ 36 = 2 remainder 33 |
| 3 | 36 ÷ 33 = 1 remainder 3 |
| 4 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 104 | 104 |
| 182 and 105 | 2730 |
| 108 and 77 | 8316 |
| 22 and 122 | 1342 |
| 199 and 84 | 16716 |