Least Common Multiple (LCM) of 19 and 59
The least common multiple (LCM) of 19 and 59 is 1121.
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 59?
First, calculate the GCD of 19 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 59 = 0 remainder 19 |
| 2 | 59 ÷ 19 = 3 remainder 2 |
| 3 | 19 ÷ 2 = 9 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 119 | 5236 |
| 24 and 42 | 168 |
| 138 and 161 | 966 |
| 108 and 150 | 2700 |
| 75 and 81 | 2025 |