Least Common Multiple (LCM) of 14 and 137
The least common multiple (LCM) of 14 and 137 is 1918.
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 14 and 137?
First, calculate the GCD of 14 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 137 = 0 remainder 14 |
| 2 | 137 ÷ 14 = 9 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 173 | 3460 |
| 110 and 64 | 3520 |
| 196 and 120 | 5880 |
| 197 and 95 | 18715 |
| 48 and 178 | 4272 |