Least Common Multiple (LCM) of 19 and 37
The least common multiple (LCM) of 19 and 37 is 703.
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 37?
First, calculate the GCD of 19 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 37 = 0 remainder 19 |
| 2 | 37 ÷ 19 = 1 remainder 18 |
| 3 | 19 ÷ 18 = 1 remainder 1 |
| 4 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 161 | 4830 |
| 182 and 131 | 23842 |
| 147 and 60 | 2940 |
| 106 and 119 | 12614 |
| 41 and 166 | 6806 |