Least Common Multiple (LCM) of 137 and 170
The least common multiple (LCM) of 137 and 170 is 23290.
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 170?
First, calculate the GCD of 137 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 170 = 0 remainder 137 |
| 2 | 170 ÷ 137 = 1 remainder 33 |
| 3 | 137 ÷ 33 = 4 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 81 | 5751 |
| 14 and 108 | 756 |
| 127 and 58 | 7366 |
| 138 and 175 | 24150 |
| 96 and 89 | 8544 |