Least Common Multiple (LCM) of 105 and 137
The least common multiple (LCM) of 105 and 137 is 14385.
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 105 and 137?
First, calculate the GCD of 105 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 137 = 0 remainder 105 |
| 2 | 137 ÷ 105 = 1 remainder 32 |
| 3 | 105 ÷ 32 = 3 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 31 | 5146 |
| 67 and 196 | 13132 |
| 65 and 55 | 715 |
| 149 and 150 | 22350 |
| 109 and 52 | 5668 |