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 |
|---|---|
| 158 and 67 | 10586 |
| 193 and 174 | 33582 |
| 114 and 32 | 1824 |
| 98 and 19 | 1862 |
| 159 and 200 | 31800 |