Least Common Multiple (LCM) of 116 and 141
The least common multiple (LCM) of 116 and 141 is 16356.
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 116 and 141?
First, calculate the GCD of 116 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 141 = 0 remainder 116 |
| 2 | 141 ÷ 116 = 1 remainder 25 |
| 3 | 116 ÷ 25 = 4 remainder 16 |
| 4 | 25 ÷ 16 = 1 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 31 | 2232 |
| 32 and 126 | 2016 |
| 10 and 184 | 920 |
| 197 and 195 | 38415 |
| 150 and 93 | 4650 |