Least Common Multiple (LCM) of 75 and 137
The least common multiple (LCM) of 75 and 137 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 75 and 137?
First, calculate the GCD of 75 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 137 = 0 remainder 75 |
| 2 | 137 ÷ 75 = 1 remainder 62 |
| 3 | 75 ÷ 62 = 1 remainder 13 |
| 4 | 62 ÷ 13 = 4 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 169 | 11999 |
| 149 and 106 | 15794 |
| 110 and 76 | 4180 |
| 126 and 88 | 5544 |
| 27 and 114 | 1026 |