Least Common Multiple (LCM) of 105 and 141
The least common multiple (LCM) of 105 and 141 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 105 and 141?
First, calculate the GCD of 105 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 141 = 0 remainder 105 |
| 2 | 141 ÷ 105 = 1 remainder 36 |
| 3 | 105 ÷ 36 = 2 remainder 33 |
| 4 | 36 ÷ 33 = 1 remainder 3 |
| 5 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 93 | 14136 |
| 113 and 157 | 17741 |
| 48 and 108 | 432 |
| 156 and 131 | 20436 |
| 77 and 200 | 15400 |