Least Common Multiple (LCM) of 117 and 19
The least common multiple (LCM) of 117 and 19 is 2223.
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 19?
First, calculate the GCD of 117 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 19 = 6 remainder 3 |
| 2 | 19 ÷ 3 = 6 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 62 | 4402 |
| 66 and 107 | 7062 |
| 94 and 111 | 10434 |
| 165 and 51 | 2805 |
| 151 and 93 | 14043 |