Least Common Multiple (LCM) of 137 and 155
The least common multiple (LCM) of 137 and 155 is 21235.
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 155?
First, calculate the GCD of 137 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 155 = 0 remainder 137 |
| 2 | 155 ÷ 137 = 1 remainder 18 |
| 3 | 137 ÷ 18 = 7 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 33 | 2706 |
| 73 and 32 | 2336 |
| 143 and 100 | 14300 |
| 137 and 67 | 9179 |
| 173 and 35 | 6055 |