Least Common Multiple (LCM) of 19 and 55
The least common multiple (LCM) of 19 and 55 is 1045.
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 55?
First, calculate the GCD of 19 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 55 = 0 remainder 19 |
| 2 | 55 ÷ 19 = 2 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 |
|---|---|
| 115 and 127 | 14605 |
| 96 and 146 | 7008 |
| 172 and 167 | 28724 |
| 179 and 137 | 24523 |
| 136 and 156 | 5304 |