Least Common Multiple (LCM) of 137 and 75
The least common multiple (LCM) of 137 and 75 is 10275.
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 75?
First, calculate the GCD of 137 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 75 = 1 remainder 62 |
| 2 | 75 ÷ 62 = 1 remainder 13 |
| 3 | 62 ÷ 13 = 4 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 122 | 10126 |
| 198 and 144 | 1584 |
| 171 and 33 | 1881 |
| 25 and 27 | 675 |
| 162 and 139 | 22518 |