Least Common Multiple (LCM) of 117 and 141
The least common multiple (LCM) of 117 and 141 is 5499.
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 117 and 141?
First, calculate the GCD of 117 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 141 = 0 remainder 117 |
| 2 | 141 ÷ 117 = 1 remainder 24 |
| 3 | 117 ÷ 24 = 4 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 193 | 5597 |
| 84 and 61 | 5124 |
| 105 and 69 | 2415 |
| 136 and 134 | 9112 |
| 89 and 79 | 7031 |