Least Common Multiple (LCM) of 137 and 103
The least common multiple (LCM) of 137 and 103 is 14111.
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 103?
First, calculate the GCD of 137 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 103 = 1 remainder 34 |
| 2 | 103 ÷ 34 = 3 remainder 1 |
| 3 | 34 ÷ 1 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 171 | 24282 |
| 75 and 44 | 3300 |
| 67 and 163 | 10921 |
| 113 and 98 | 11074 |
| 193 and 12 | 2316 |