Least Common Multiple (LCM) of 137 and 19
The least common multiple (LCM) of 137 and 19 is 2603.
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 137 and 19?
First, calculate the GCD of 137 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 19 = 7 remainder 4 |
| 2 | 19 ÷ 4 = 4 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 57 | 3306 |
| 102 and 45 | 1530 |
| 16 and 38 | 304 |
| 113 and 110 | 12430 |
| 27 and 80 | 2160 |