Least Common Multiple (LCM) of 19 and 118
The least common multiple (LCM) of 19 and 118 is 2242.
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 118?
First, calculate the GCD of 19 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 118 = 0 remainder 19 |
| 2 | 118 ÷ 19 = 6 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 65 | 130 |
| 158 and 52 | 4108 |
| 44 and 31 | 1364 |
| 181 and 132 | 23892 |
| 121 and 46 | 5566 |