Least Common Multiple (LCM) of 19 and 93
The least common multiple (LCM) of 19 and 93 is 1767.
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 19 and 93?
First, calculate the GCD of 19 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 93 = 0 remainder 19 |
| 2 | 93 ÷ 19 = 4 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 141 | 15087 |
| 152 and 112 | 2128 |
| 54 and 189 | 378 |
| 148 and 145 | 21460 |
| 78 and 19 | 1482 |